Workshop 1 - Linear models
22 novembre, 2019
Links:
Examples of Stan code for regression models
What is in the stan fit object?
1 Data set Howell
Dataset Howell from the rethinking package.
data(Howell1)
howell1 <- Howell1
head(howell1)## height weight age male
## 1 151.765 47.82561 63 1
## 2 139.700 36.48581 63 0
## 3 136.525 31.86484 65 0
## 4 156.845 53.04191 41 1
## 5 145.415 41.27687 51 0
## 6 163.830 62.99259 35 1str(howell1)## 'data.frame': 544 obs. of 4 variables:
## $ height: num 152 140 137 157 145 ...
## $ weight: num 47.8 36.5 31.9 53 41.3 ...
## $ age : num 63 63 65 41 51 35 32 27 19 54 ...
## $ male : int 1 0 0 1 0 1 0 1 0 1 ...ggplot(howell1, aes(height),bins=50) + geom_histogram(aes(y = ..count..), fill="darkgreen",binwidth = 1, alpha=0.4) +
theme(axis.line = element_line(size=1, colour = "black"),
panel.grid.major = element_line(colour = "#d3d3d3"),
panel.grid.minor = element_blank())
Subset with only individuals over 18 years old:
howell2 <- howell1[howell1$age >= 18 , ]plot_grid(ggplot(howell2, aes(height),bins=50) + geom_histogram(aes(y = ..count..), fill="darkgreen",binwidth = 1, alpha=0.4) +
theme(axis.line = element_line(size=1, colour = "black"),
panel.grid.major = element_line(colour = "#d3d3d3"),
panel.grid.minor = element_blank()),
ggplot(howell2, aes(weight),bins=50) + geom_histogram(aes(y = ..count..), fill="blue",binwidth = 1, alpha=0.4) +
theme(axis.line = element_line(size=1, colour = "black"),
panel.grid.major = element_line(colour = "#d3d3d3"),
panel.grid.minor = element_blank()))
ggplot(howell2,aes(y=height,x=weight))+geom_point() + theme(axis.line = element_line(size=1, colour = "black"),
panel.grid.major = element_line(colour = "gray95"),
panel.grid.minor = element_blank())
2 Without predictor
2.1 With large variance
\[ h_{i} \sim \mathcal{N}(\mu \, , \, \sigma^2)\] \[\mu \sim \mathcal{N}(178,20)\]
Data in a list:
m1.data <- list(N = nrow(howell2), height = howell2$height)2.1.1 Notation 1 (vectorized with target += notation)
explicitly incrementing the log probability function
https://mc-stan.org/docs/2_18/reference-manual/increment-log-prob-section.html
“The basis of Stan’s execution is the evaluation of a log probability function (specifically, a probability density function) for a given set of (real-valued) parameters; this function returns the log density of the posterior up to an additive constant. Data and transformed data are fixed before the log density is evaluated. The total log probability is initialized to zero. Next, any log Jacobian adjustments accrued by the variable constraints are added to the log density (the Jacobian adjustment may be skipped for optimization). Sampling and log probability increment statements may add to the log density in the model block. A log probability increment statement directly increments the log density with the value of an expression as follows.”
https://stackoverflow.com/questions/40289457/stan-using-target-syntax
“The target density is the density from which the sampler samples and it needs to be equal to the joint density of all the parameters given the data up to a constant (which is usually achieved via Bayes’s rule by coding as the joint density of parameters and modeled data up to a constant).”
data { // observed variables
int<lower=1> N; // number of observations
vector[N] height; // response variables
}
parameters { // unobserved variables
real mu;
real<lower=0,upper=50> sigma;
}
model {
target += normal_lpdf(height | mu, sigma); // likelihood
target += normal_lpdf(mu | 178, 20); // prior of the mean
}fit.m1.1 <- sampling(m1.1, data = m1.data, iter = 1000, chains = 2, cores = 2)
print(fit.m1.1, probs = c(0.10, 0.5, 0.9))## Inference for Stan model: bb69f84792e053a2e0234193f5617c02.
## 2 chains, each with iter=1000; warmup=500; thin=1;
## post-warmup draws per chain=500, total post-warmup draws=1000.
##
## mean se_mean sd 10% 50% 90% n_eff Rhat
## mu 154.60 0.01 0.39 154.10 154.61 155.09 992 1
## sigma 7.77 0.01 0.30 7.39 7.76 8.14 1086 1
## lp__ -1223.07 0.04 0.92 -1224.25 -1222.81 -1222.22 523 1
##
## Samples were drawn using NUTS(diag_e) at Thu Nov 7 13:58:01 2019.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).2.1.2 Notation 2 (vectorized with Jags-like notation)
using the sampling statement
Difference with explicitly incrementing the log probability function:
“The sampling statement drops all the terms in the log probability function that are constant, whereas the explicit call to normal_lpdf adds all of the terms in the definition of the log normal probability function, including all of the constant normalizing terms. Therefore, the explicit increment form can be used to recreate the exact log probability values for the model. Otherwise, the sampling statement form will be faster if any of the input expressions involve only constants, data variables, and transformed data variables.”
https://mc-stan.org/docs/2_18/reference-manual/sampling-statements-section.html
Bounding sigma in the parameter block:
data { // observed variables
int<lower=1> N; // number of observations
vector[N] height; // response variables
}
parameters { // unobserved variables
real mu;
real<lower=0,upper=50> sigma;
}
model {
height ~ normal(mu,sigma); // likelihood
mu ~ normal(178, 20); // prior of the mean
}fit.m1.2.1 <- sampling(m1.2.1, data = m1.data, iter = 1000, chains = 2, cores = 2)
print(fit.m1.2.1, probs = c(0.10, 0.5, 0.9))## Inference for Stan model: 362449507f9771e1464afdb2ddaff73e.
## 2 chains, each with iter=1000; warmup=500; thin=1;
## post-warmup draws per chain=500, total post-warmup draws=1000.
##
## mean se_mean sd 10% 50% 90% n_eff Rhat
## mu 154.62 0.01 0.40 154.09 154.63 155.14 1003 1
## sigma 7.76 0.01 0.29 7.40 7.76 8.13 904 1
## lp__ -895.71 0.04 0.90 -896.94 -895.48 -894.85 455 1
##
## Samples were drawn using NUTS(diag_e) at Thu Nov 7 13:58:30 2019.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).Specifying the prior of sigma in the model block (\(\sigma \sim \mathcal{U}(0,50)\)):
data { // observed variables
int<lower=1> N; // number of observations
vector[N] height; // response variables
}
parameters { // unobserved variables
real mu;
real sigma;
}
model {
height ~ normal(mu,sigma); // likelihood
mu ~ normal(178, 20); // prior of the mean
sigma ~ uniform(0,50); // prior of sigma
}fit.m1.2.2 <- sampling(m1.2.2, data = m1.data, iter = 1000, chains = 2, cores = 2)
print(fit.m1.2.2, probs = c(0.10, 0.5, 0.9))## Inference for Stan model: a7cb2ed5bc279b99bc559cfdb30b62e2.
## 2 chains, each with iter=1000; warmup=500; thin=1;
## post-warmup draws per chain=500, total post-warmup draws=1000.
##
## mean se_mean sd 10% 50% 90% n_eff Rhat
## mu 154.60 0.02 0.41 154.11 154.60 155.13 708 1.00
## sigma 7.77 0.01 0.30 7.40 7.75 8.17 779 1.00
## lp__ -895.75 0.05 1.01 -897.15 -895.44 -894.84 447 1.01
##
## Samples were drawn using NUTS(diag_e) at Thu Nov 7 13:59:01 2019.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).2.1.3 Notation 3 (unvectorized)
data { // observed variables
int<lower=1> N; // number of observations
vector[N] height; // response variables
}
parameters { // unobserved variables
real mu;
real<lower=0,upper=50> sigma;
}
model {
for (n in 1:N)
height[n] ~ normal(mu,sigma); // likelihood
mu ~ normal(178, 20); // prior of the mean
}fit.m1.3 <- sampling(m1.3, data = m1.data, iter = 1000, chains = 2, cores = 2)
print(fit.m1.3, probs = c(0.10, 0.5, 0.9))## Inference for Stan model: 2c0d3bdaed726863b2342ed270e93080.
## 2 chains, each with iter=1000; warmup=500; thin=1;
## post-warmup draws per chain=500, total post-warmup draws=1000.
##
## mean se_mean sd 10% 50% 90% n_eff Rhat
## mu 154.62 0.01 0.41 154.10 154.62 155.16 1015 1.00
## sigma 7.77 0.01 0.29 7.38 7.76 8.14 1083 1.00
## lp__ -895.74 0.04 0.94 -896.94 -895.49 -894.85 479 1.01
##
## Samples were drawn using NUTS(diag_e) at Thu Nov 7 13:59:31 2019.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).2.1.3.1 Comparing model runtime
Vectorized with target += notation:
get_elapsed_time(fit.m1.1)## warmup sample
## chain:1 0.017447 0.007627
## chain:2 0.015749 0.006771Vectorized with Jags-like notation:
# not specifying the prior of sigma
get_elapsed_time(fit.m1.2.1)## warmup sample
## chain:1 0.015877 0.007393
## chain:2 0.017561 0.008066# Specifying the prior of sigma
get_elapsed_time(fit.m1.2.2)## warmup sample
## chain:1 0.018798 0.008674
## chain:2 0.014649 0.007995Unvectorized:
get_elapsed_time(fit.m1.3)## warmup sample
## chain:1 0.055097 0.039766
## chain:2 0.054672 0.0289022.2 With low variance
\[ h_{i} \sim \mathcal{N}(\mu \, , \, \sigma^2)\] \[\mu \sim \mathcal{N}(178,0.1)\]
Data in a list:
m2.data <- list(N = nrow(howell2), height = howell2$height)data { // observed variables
int<lower=1> N; // number of observations
vector[N] height; // response variables
}
parameters { // unobserved variables
real mu;
real<lower=0,upper=50> sigma;
}
model {
target += normal_lpdf(height | mu, sigma); // likelihood
target += normal_lpdf(mu | 178, 0.1); // prior of the mean
}fit.m2 <- sampling(m2 , data = m2.data, iter = 1000, chains = 2, cores = 2)
print(fit.m2, probs = c(0.10, 0.5, 0.9))## Inference for Stan model: 732cdcf02bdc315da3f0b397f4c17596.
## 2 chains, each with iter=1000; warmup=500; thin=1;
## post-warmup draws per chain=500, total post-warmup draws=1000.
##
## mean se_mean sd 10% 50% 90% n_eff Rhat
## mu 177.87 0.00 0.10 177.74 177.86 178.00 935 1
## sigma 24.63 0.03 0.91 23.45 24.59 25.85 909 1
## lp__ -1623.63 0.05 0.98 -1624.97 -1623.34 -1622.77 424 1
##
## Samples were drawn using NUTS(diag_e) at Thu Nov 7 14:00:01 2019.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).3 With one continious predictor
Model equation:
\[\begin{align*} h_{i} \sim & \, \mathcal{N}(\mu_{i} \, , \, \sigma^2) \\[4pt] \mu_{i} = & \, \beta_{1} + \beta_{2} w_{i}\\[4pt] \beta_{1} \sim & \, \mathcal{N}(178,100)\\[4pt] \beta_{2} \sim & \, \mathcal{N}(0,10)\\[4pt] \sigma \sim & \, \mathcal{U}(0,5)\\[4pt] \end{align*}\]Centering the predictor:
howell2$weight.c <- howell2$weight - mean(howell2$weight)Data in a list:
m3.data <- list(N = nrow(howell2), height = howell2$height, weight = howell2$weight.c)data { // observed variables
int<lower=1> N; // number of observations
vector[N] height; // response variables
vector[N] weight; // predictor (previously centered)
}
parameters { // unobserved variables
real beta[2]; // parameters: intercept and slopes
real sigma;
}
model {
height ~ normal(beta[1] + beta[2]*weight ,sigma); // likelihood
beta[1] ~ normal(178, 100); // prior of the intercept
beta[2] ~ normal(0, 10); // prior of the slope
sigma ~ uniform(0,50);
}fit.m3.1 <- sampling(m3.1, data = m3.data, iter = 1000, chains = 4, cores = 4)
print(fit.m3.1, probs = c(0.10, 0.5, 0.9))## Inference for Stan model: 2c0bf7468a6290532584633469739fd9.
## 4 chains, each with iter=1000; warmup=500; thin=1;
## post-warmup draws per chain=500, total post-warmup draws=2000.
##
## mean se_mean sd 10% 50% 90% n_eff Rhat
## beta[1] 154.60 0.01 0.28 154.25 154.60 154.95 2358 1
## beta[2] 0.91 0.00 0.04 0.85 0.90 0.96 1613 1
## sigma 5.11 0.00 0.20 4.87 5.10 5.36 2058 1
## lp__ -747.63 0.04 1.26 -749.20 -747.29 -746.40 992 1
##
## Samples were drawn using NUTS(diag_e) at Thu Nov 7 15:43:53 2019.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).Another possibility for \(\beta_{2}\) prior: \[\beta_{2} \sim \, \text{LogNormal}(0,10)\].
data { // observed variables
int<lower=1> N; // number of observations
vector[N] height; // response variables
vector[N] weight; // predictor (previously centered)
}
parameters { // unobserved variables
real beta[2]; // parameters: intercept and slopes
real sigma;
}
model {
height ~ normal(beta[1] + beta[2]*weight ,sigma); // likelihood
beta[1] ~ normal(178, 100); // prior of the intercept
beta[2] ~ lognormal(0, 1); // prior of the slope
sigma ~ uniform(0,50);
}fit.m3.2 <- sampling(m3.2, data = m3.data, iter = 1000, chains = 4, cores = 4)
print(fit.m3.2, probs = c(0.10, 0.5, 0.9))## Inference for Stan model: 33297718f34e2620ae7a419b4225e246.
## 4 chains, each with iter=1000; warmup=500; thin=1;
## post-warmup draws per chain=500, total post-warmup draws=2000.
##
## mean se_mean sd 10% 50% 90% n_eff Rhat
## beta[1] 154.61 0.01 0.27 154.25 154.61 154.95 1921 1
## beta[2] 0.90 0.00 0.04 0.85 0.90 0.96 2063 1
## sigma 5.11 0.00 0.20 4.85 5.10 5.36 2089 1
## lp__ -747.51 0.04 1.24 -749.16 -747.20 -746.28 1049 1
##
## Samples were drawn using NUTS(diag_e) at Thu Nov 7 15:44:27 2019.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).vectorized with target +=
data { // observed variables
int<lower=1> N; // number of observations
vector[N] height; // response variables
vector[N] weight; // predictor (previously centered)
}
parameters { // unobserved variables
real beta[2]; // parameters: intercept and slopes
real sigma;
}
model {
target += normal_lpdf(height | beta[1] + beta[2]*weight, sigma); // likelihood
target += normal_lpdf(beta[1] | 178, 20); // prior of the intercept
target += lognormal_lpdf(beta[2] |0, 1); // prior of the slope
target += uniform_lpdf(sigma|0,50);
}fit.m3.3 <- sampling(m3.3, data = m3.data, iter = 1000, chains = 4, cores = 4)
print(fit.m3.3, probs = c(0.10, 0.5, 0.9))## Inference for Stan model: 75d942089dad056ec9f4c75cf887e097.
## 4 chains, each with iter=1000; warmup=500; thin=1;
## post-warmup draws per chain=500, total post-warmup draws=2000.
##
## mean se_mean sd 10% 50% 90% n_eff Rhat
## beta[1] 154.60 0.01 0.27 154.26 154.59 154.94 1705 1
## beta[2] 0.90 0.00 0.04 0.85 0.91 0.96 1460 1
## sigma 5.10 0.00 0.19 4.87 5.09 5.35 1945 1
## lp__ -1080.32 0.04 1.22 -1081.92 -1080.02 -1079.17 881 1
##
## Samples were drawn using NUTS(diag_e) at Thu Nov 7 18:39:08 2019.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).3.1 What do our priors imply?
Let’s simulate the prior predictive distribution (simulate heights from the model, using only the priors).
See Chapter 4 of Statistical Rethinking.
set.seed(2971)
N <- 100 # 100 lines
a <- rnorm( N , 178 , 20 )
b1 <- rnorm( N , 0 , 10 )
b2 <- rlnorm( N, 0 , 1 )
dens(rnorm( 1e4, 0 , 10 ),main="b ~ dnorm(0,10)")
dens(rlnorm( 1e4 , 0 , 1 ),main="log(b) ~ dnorm(0,1)")
p <- plot( NULL , xlim=range(howell2$weight) , ylim=c(-100,400) ,xlab="weight" , ylab="height")
abline(h=0,lty=2)
abline( h=272 , lty=1 , lwd=0.5 )
mtext( "b ~ dnorm(0,10)" )
xbar <- mean(howell2$weight)
for ( i in 1:N ) curve( a[i] + b1[i]*(x - xbar) ,
from=min(howell2$weight) , to=max(howell2$weight) , add=TRUE ,
col=col.alpha("black",0.2) )
McElreath: “For reference, I’ve added a dashed line at zero—no one is shorter than zero—and the “Wadlow” line at 272cm for the world’s tallest person. The pattern doesn’t look like any human population at all. It essentially says that the relationship between weight and height could be absurdly positive or negative. Before we’ve even seen the data, this is a bad model.”
plot( NULL , xlim=range(howell2$weight) , ylim=c(-100,400) ,xlab="weight" , ylab="height")
abline(h=0,lty=2)
abline( h=272 , lty=1 , lwd=0.5 )
mtext( "log(b) ~ dnorm(0,1)" )
xbar <- mean(howell2$weight)
for ( i in 1:N ) curve( a[i] + b2[i]*(x - xbar) ,
from=min(howell2$weight) , to=max(howell2$weight) , add=TRUE ,
col=col.alpha("black",0.2) )
McElreath: “This is much more sensible. There is still a rare impossible relationship. But nearly all lines in the joint prior for \(\beta_{1}\) and \(\beta_{2}\) are now within human reason. We’re fussing about this prior, even though as you’ll see in the next section there is so much data in this example that the priors end up not mattering. We fuss for two reasons. First, there are many analyses in which no amount of data makes the prior irrelevant. In such cases, non-Bayesian procedures are no better off. They also depend upon structural features of the model. Paying careful attention to those features is essential. Second, thinking about the priors helps us develop better models, maybe even eventually going beyond geocentrism.”
Help to choose your prior with Stan: https://github.com/stan-dev/stan/wiki/Prior-Choice-Recommendations
3.2 Convergence diagnostics
https://github.com/stan-dev/stan/wiki/Stan-Best-Practices
3.2.1 Rhat < 1.1
“The best generic diagnostic for the accuracy of a Markov chain Monte Carlo algorithm is the split R-hat statistic which quantifies the consistency of an ensemble of Markov chains. The idea is to run multiple Markov chains, 4 is an okay default but running more makes the diagnostic more sensitive, and ensure that they’re all exploring the same regions of parameter space. If even one chain is inconsistent with the others then all of the chains are suspect! In practice we have found that requiring Rhat < 1.1 is a good default requirement for each parameter.”
rhats <- rhat(fit.m3.2)
print(rhats)## beta[1] beta[2] sigma lp__
## 0.9988572 0.9988693 0.9996734 1.0029385mcmc_rhat(rhats) + yaxis_text(hjust = 1)
3.2.2 Effective sample size
“Another potential problem to keep in mind is Markov chains that explore very slowly. Slow chains lead to low numbers of effective samples, and if there are too few effective samples then we can’t accurate estimate the number of effective samples at all. A good check for such issues is the number of effective samples per iteration – if N_eff / N < 0.001 then you should be suspect of the effective sample size calculation.”
ratios <- neff_ratio(fit.m3.2)
print(ratios)## beta[1] beta[2] sigma lp__
## 0.9604525 1.0316468 1.0444858 0.5245081mcmc_neff(ratios, size = 2)
3.2.3 MCMC diagnostics using the bayesplot package
We need:
# The posterior draws
posterior <- as.array(fit.m3.2)
# The log of the posterior density for each draw
lp <- log_posterior(fit.m3.2)
head(lp)## Iteration Value Chain
## 1 1 -746.9374 1
## 2 2 -747.6230 1
## 3 3 -748.4853 1
## 4 4 -747.0805 1
## 5 5 -746.8393 1
## 6 6 -746.6638 1# Some NUTS-specific diagnostic values
np <- nuts_params(fit.m3.2)
head(np)## Iteration Parameter Value Chain
## 1 1 accept_stat__ 0.8870933 1
## 2 2 accept_stat__ 0.7779165 1
## 3 3 accept_stat__ 0.8750988 1
## 4 4 accept_stat__ 1.0000000 1
## 5 5 accept_stat__ 0.9889832 1
## 6 6 accept_stat__ 0.9230367 13.2.3.1 Divergent transitions
https://mc-stan.org/bayesplot/articles/visual-mcmc-diagnostics.html
mcmc_parcoord(posterior, np = np,pars=c("beta[1]","beta[2]","sigma"))
Pairs plots:
mcmc_pairs(posterior, np = np, pars = c("beta[1]","beta[2]","sigma"), off_diag_args = list(size = 0.75))
Trace plots:
mcmc_trace(posterior, pars = "beta[2]", np = np) + xlab("Post-warmup iteration")## No divergences to plot.
3.3 Posterior predictive distributions
https://mc-stan.org/docs/2_18/stan-users-guide/prediction-forecasting-and-backcasting.html
m4.data <- list(N = nrow(howell2), height = howell2$height, weight = howell2$weight.c)data { // observed variables
int<lower=1> N; // number of observations
vector[N] height; // response variables
vector[N] weight; // predictor (previously centered)
}
parameters { // unobserved variables
real beta[2]; // parameters: intercept and slope
real sigma;
}
model {
height ~ normal(beta[1] + beta[2]*weight ,sigma); // likelihood
beta[1] ~ normal(178, 100); // prior of the intercept
beta[2] ~ lognormal(0, 1); // prior of the slope
sigma ~ uniform(0,50);
}
generated quantities {
vector[N] y_rep;
for(i in 1:N)
y_rep[i] = normal_rng(beta[1] + beta[2]*weight[i], sigma);
}fit.m4 <- sampling(m4, data = m4.data, iter = 1000, chains = 4, cores = 4)
y_rep <- as.matrix(fit.m4, pars = "y_rep")
dim(y_rep)## [1] 2000 352ppc_dens_overlay(howell2$height, y_rep)
plot_grid(ppc_stat(y = howell2$height, yrep = y_rep, stat = "mean"),
ppc_scatter_avg(y = howell2$height, yrep = y_rep))
3.4 Visualizing the variance
See section 4.4 of Statistical rethinking
Model with non-centered weight:
m3.1.bis.data <- list(N = nrow(howell2), height = howell2$height, weight = howell2$weight)data { // observed variables
int<lower=1> N; // number of observations
vector[N] height; // response variables
vector[N] weight; // predictor (previously centered)
}
parameters { // unobserved variables
real beta[2]; // parameters: intercept and slopes
real sigma;
}
model {
height ~ normal(beta[1] + beta[2]*weight ,sigma); // likelihood
beta[1] ~ normal(178, 100); // prior of the intercept
beta[2] ~ normal(0, 10); // prior of the slope
sigma ~ uniform(0,50);
}fit.m3.1.bis <- sampling(m3.1.bis, data = m3.1.bis.data, iter = 1000, chains = 4, cores = 4)
print(fit.m3.1.bis, probs = c(0.10, 0.5, 0.9))## Inference for Stan model: dca6bb84ed30c87a7015873cc74526bf.
## 4 chains, each with iter=1000; warmup=500; thin=1;
## post-warmup draws per chain=500, total post-warmup draws=2000.
##
## mean se_mean sd 10% 50% 90% n_eff Rhat
## beta[1] 113.90 0.08 1.96 111.32 113.86 116.45 660 1
## beta[2] 0.90 0.00 0.04 0.85 0.91 0.96 653 1
## sigma 5.11 0.01 0.20 4.86 5.11 5.37 743 1
## lp__ -749.32 0.05 1.23 -751.07 -749.03 -748.06 685 1
##
## Samples were drawn using NUTS(diag_e) at Fri Nov 22 14:35:54 2019.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).3.4.1 Prediction interval for average height
Figure 4.7. of Statistical rethinking
post <- as.data.frame(fit.m3.1.bis)
f_mu <- function(x) post$`beta[1]` + post$`beta[2]` * x
weight_new <- seq(25, 70)
mu <-
sapply(weight_new, f_mu) %>%
tibble::as_tibble() %>%
rename_all(function(x) weight_new) %>%
mutate(Iter = row_number()) %>%
gather(weight, height, -Iter) %>%
group_by(weight) %>%
mutate(hpdi_l = HDInterval::hdi(height, credMass = 0.89)[1],
hpdi_h = HDInterval::hdi(height, credMass = 0.89)[2]) %>%
mutate(mu = mean(height)) %>%
ungroup() %>%
mutate(weight = as.integer(weight))
p <- ggplot()
p1 <- p +
geom_point(data = mu %>% filter(Iter < 101),
aes(weight, height), alpha = .05, color = 'dodgerblue') +
labs(subtitle="Density at each weight")
p2 <- p +
geom_point(data = howell2,
aes(weight, height), shape = 1, color = 'dodgerblue') +
geom_ribbon(data = mu,
aes(x = weight, ymin = hpdi_l, ymax = hpdi_h),
alpha = .2) +
geom_abline(data = post,
aes(intercept = mean(`beta[1]`), slope = mean(`beta[2]`))) +
labs(subtitle="HPDI Interval = 0.89")
grid.arrange(p1, p2, nrow = 1) 
“Left: The first 100 values in the distribution of \(\beta_{1}\) (intercept) at each weight value. Right: The !Kung height data again, now with 89% HPDI of the mean indicated by the shaded region. Compare this region to the distributions of blue points on the left.”
3.4.2 Prediction interval for actual heights
Figure 4.8. of Statistical rethinking
Incorporating the uncertainty related to the standard deviation \(\sigma^{2}\).
sim_ht <-
sapply(weight_new,
function(x)
rnorm(NROW(post),
post$`beta[1]` + post$`beta[2]` * x,
post$sigma)) %>%
as_tibble() %>%
rename_all(function(x) weight_new) %>%
mutate(Iter = row_number()) %>%
gather(weight, height, -Iter) %>%
group_by(weight) %>%
mutate(pi_l = rethinking::PI(height, prob = 0.89)[1],
pi_h = rethinking::PI(height, prob = 0.89)[2]) %>%
ungroup() %>%
mutate(weight = as.integer(weight))
p2 + geom_ribbon(data = sim_ht,
mapping = aes(x=weight, ymin=pi_l, ymax=pi_h), alpha = .1) +
labs(subtitle = 'Prediction Intervals = 0.89')
“Figure 4.8. 89% prediction interval for height, as a function of weight. The solid line is the MAP estimate of the mean height at each weight. The two shaded regions show different 89% plausible regions. The narrow shaded interval around the line is the distribution of \(\beta_{1}\) (intercept) . The wider shaded region represents the region within which the model expects to find 89% of actual heights in the population, at each weight.”"
4 With one categorical predictor
Individual sex is a categorical variable with value 0 whenever the person is a female and a value 1 whenever the person is a male.
ggplot(howell2, aes(x=as.factor(male), y=height, color=as.factor(male))) +
geom_boxplot() + scale_x_discrete(labels=c("0" = "Female", "1" = "Male")) +
theme(axis.title.x=element_blank(),legend.position = "none")
There are two ways to include binary categorical variables, either using indicator variable or index variable. More details in section 5.3.1 of Statistical rethinking (McElreath’s book).
4.1 Indicator variable (or dummy variable)
Using indicator variables is ok with binary variables, but shouldn’t be used for variables with many categories (see 5.3.2 section of Statistical rethiking).
Model equation (like in McElreath’s book):
\[\begin{align*} h_{i} &\sim \mathcal{N}(\mu_{i} \, , \, \sigma^2) \\[4pt] \mu_{i} &= \alpha + \beta_{m} m_{i}\\[4pt] \alpha &\sim \mathcal{N}(178,20)\\[4pt] \beta_{m} &\sim \mathcal{N}(0,10)\\[4pt] \sigma &\sim \mathcal{U}(0,50)\\[4pt] \end{align*}\]In R, we can convert our categorical variable in a dummy variable like this:
X <- model.matrix(~male, howell2)m5.1.data <- list(N = nrow(howell2), height = howell2$height, X = X, n = length(unique(howell2$male)))
str(m5.1.data)## List of 4
## $ N : int 352
## $ height: num [1:352] 152 140 137 157 145 ...
## $ X : num [1:352, 1:2] 1 1 1 1 1 1 1 1 1 1 ...
## ..- attr(*, "dimnames")=List of 2
## .. ..$ : chr [1:352] "1" "2" "3" "4" ...
## .. ..$ : chr [1:2] "(Intercept)" "male"
## ..- attr(*, "assign")= int [1:2] 0 1
## $ n : int 2data {
int<lower=0> N; // number of observations
int<lower=0> n; // number of levels of the categorical variable
vector[N] height; // response variables
matrix[N,n] X; // categorical variable
}
parameters {
vector[n] beta; // intercepts of the categorical variable
real sigma;
}
transformed parameters {
vector[N] mu;
mu = X*beta;
}
model {
height ~ normal(mu ,sigma); // likelihood
sigma ~ uniform(0,50);
beta[1] ~ normal(178,20);
beta[2] ~ normal(0,10);
}
generated quantities {
vector[N] y_rep;
for(i in 1:N)
y_rep[i] = normal_rng(mu[i], sigma);
}
fit.m5_1_1 <- sampling(m5.1.1, data = m5.1.data, iter = 1000, chains = 4, cores = 4)
print(fit.m5_1_1, probs = c(0.10, 0.5, 0.9))## Inference for Stan model: a89cc41ee4ed1022b476f4484ab5720d.
## 4 chains, each with iter=1000; warmup=500; thin=1;
## post-warmup draws per chain=500, total post-warmup draws=2000.
##
## mean se_mean sd 10% 50% 90% n_eff Rhat
## beta[1] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## beta[2] 10.83 0.03 0.60 10.09 10.85 11.58 376 1.00
## sigma 5.57 0.00 0.21 5.29 5.56 5.84 1893 1.00
## mu[1] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[2] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[3] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[4] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[5] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[6] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[7] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[8] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[9] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[10] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[11] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[12] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[13] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[14] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[15] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[16] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[17] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[18] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[19] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[20] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[21] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[22] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[23] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[24] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[25] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[26] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[27] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[28] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[29] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[30] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[31] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[32] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[33] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[34] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[35] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[36] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[37] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[38] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[39] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[40] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[41] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[42] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[43] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[44] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[45] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[46] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[47] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[48] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[49] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[50] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[51] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[52] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[53] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[54] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[55] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[56] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[57] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[58] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[59] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[60] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[61] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[62] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[63] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[64] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[65] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[66] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[67] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[68] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[69] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[70] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[71] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[72] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[73] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[74] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[75] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[76] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[77] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[78] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[79] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[80] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[81] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[82] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[83] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[84] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[85] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[86] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[87] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[88] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[89] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[90] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[91] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[92] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[93] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[94] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[95] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[96] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[97] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[98] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[99] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[100] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[101] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[102] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[103] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[104] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[105] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[106] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[107] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[108] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[109] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[110] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[111] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[112] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[113] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[114] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[115] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[116] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[117] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[118] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[119] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[120] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[121] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[122] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[123] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[124] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[125] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[126] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[127] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[128] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[129] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[130] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[131] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[132] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[133] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[134] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[135] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[136] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[137] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[138] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[139] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[140] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[141] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[142] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[143] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[144] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[145] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[146] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[147] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[148] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[149] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[150] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[151] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[152] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[153] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[154] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[155] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[156] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[157] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[158] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[159] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[160] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[161] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[162] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[163] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[164] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[165] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[166] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[167] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[168] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[169] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[170] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[171] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[172] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[173] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[174] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[175] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[176] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[177] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[178] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[179] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[180] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[181] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[182] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[183] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[184] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[185] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[186] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[187] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[188] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[189] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[190] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[191] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[192] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[193] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[194] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[195] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[196] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[197] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[198] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[199] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[200] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[201] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[202] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[203] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[204] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[205] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[206] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[207] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[208] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[209] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[210] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[211] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[212] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[213] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[214] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[215] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[216] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[217] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[218] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[219] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[220] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[221] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[222] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[223] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[224] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[225] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[226] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[227] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[228] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[229] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[230] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[231] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[232] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[233] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[234] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[235] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[236] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[237] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[238] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[239] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[240] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[241] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[242] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[243] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[244] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[245] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[246] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[247] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[248] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[249] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[250] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[251] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[252] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[253] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[254] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[255] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[256] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[257] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[258] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[259] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[260] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[261] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[262] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[263] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[264] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[265] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[266] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[267] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[268] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[269] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[270] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[271] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[272] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[273] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[274] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[275] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[276] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[277] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[278] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[279] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[280] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[281] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[282] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[283] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[284] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[285] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[286] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[287] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[288] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[289] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[290] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[291] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[292] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[293] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[294] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[295] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[296] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[297] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[298] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[299] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[300] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[301] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[302] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[303] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[304] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[305] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[306] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[307] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[308] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[309] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[310] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[311] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[312] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[313] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[314] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[315] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[316] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[317] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[318] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[319] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[320] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[321] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[322] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[323] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[324] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[325] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[326] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[327] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[328] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[329] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[330] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[331] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[332] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[333] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[334] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[335] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[336] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[337] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[338] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[339] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[340] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[341] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[342] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[343] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[344] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[345] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[346] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[347] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[348] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[349] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[350] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## mu[351] 149.53 0.02 0.40 149.01 149.52 150.05 630 1.00
## mu[352] 160.36 0.02 0.43 159.82 160.36 160.91 564 1.00
## y_rep[1] 160.28 0.12 5.58 153.28 160.29 167.40 2102 1.00
## y_rep[2] 149.51 0.13 5.71 142.28 149.45 156.94 1966 1.00
## y_rep[3] 149.37 0.12 5.49 142.17 149.50 156.50 2013 1.00
## y_rep[4] 160.18 0.13 5.64 153.01 160.25 167.34 1954 1.00
## y_rep[5] 149.74 0.12 5.63 142.35 149.82 156.83 2138 1.00
## y_rep[6] 160.22 0.12 5.67 152.95 160.31 167.10 2180 1.00
## y_rep[7] 149.36 0.13 5.60 142.37 149.22 156.34 1753 1.00
## y_rep[8] 160.47 0.14 5.69 153.16 160.45 167.95 1703 1.00
## y_rep[9] 149.49 0.13 5.65 142.24 149.48 156.83 1862 1.00
## y_rep[10] 160.49 0.14 5.58 153.52 160.47 167.57 1682 1.00
## y_rep[11] 149.35 0.12 5.48 142.34 149.41 156.21 1966 1.00
## y_rep[12] 160.38 0.12 5.58 153.23 160.34 167.56 2008 1.00
## y_rep[13] 149.45 0.12 5.48 142.62 149.47 156.44 1923 1.00
## y_rep[14] 149.51 0.14 5.66 142.23 149.41 156.79 1729 1.00
## y_rep[15] 149.54 0.13 5.53 142.50 149.54 156.81 1830 1.00
## y_rep[16] 160.30 0.13 5.58 153.32 160.33 167.44 1807 1.00
## y_rep[17] 160.34 0.13 5.58 153.16 160.24 167.54 1957 1.00
## y_rep[18] 149.52 0.12 5.50 142.30 149.87 156.50 2049 1.00
## y_rep[19] 160.32 0.13 5.41 153.43 160.30 167.34 1723 1.00
## y_rep[20] 149.80 0.13 5.56 142.71 149.89 156.59 1938 1.00
## y_rep[21] 160.53 0.12 5.58 153.33 160.53 167.41 2159 1.00
## y_rep[22] 149.52 0.12 5.45 142.49 149.61 156.60 1958 1.00
## y_rep[23] 149.69 0.13 5.67 142.58 149.61 157.08 1892 1.00
## y_rep[24] 160.60 0.13 5.57 153.52 160.61 168.04 1846 1.00
## y_rep[25] 160.45 0.12 5.39 153.50 160.56 167.20 2030 1.00
## y_rep[26] 149.46 0.13 5.63 142.11 149.35 156.60 1943 1.00
## y_rep[27] 149.67 0.12 5.59 142.58 149.53 156.70 2024 1.00
## y_rep[28] 149.77 0.12 5.59 142.56 149.95 156.85 2143 1.00
## y_rep[29] 149.68 0.13 5.54 142.60 149.87 156.77 1884 1.00
## y_rep[30] 149.57 0.12 5.48 142.42 149.65 156.78 2042 1.00
## y_rep[31] 149.77 0.12 5.61 142.72 149.82 156.89 2125 1.00
## y_rep[32] 160.31 0.13 5.73 153.04 160.30 167.55 1983 1.00
## y_rep[33] 160.60 0.13 5.64 153.54 160.60 167.84 1937 1.00
## y_rep[34] 160.10 0.12 5.56 153.12 160.09 167.16 2114 1.00
## y_rep[35] 160.28 0.13 5.53 153.40 160.07 167.57 1904 1.00
## y_rep[36] 149.63 0.13 5.51 142.81 149.55 156.76 1860 1.00
## y_rep[37] 149.59 0.12 5.67 142.25 149.42 156.84 2082 1.00
## y_rep[38] 160.49 0.13 5.66 153.22 160.44 167.89 1962 1.00
## y_rep[39] 149.50 0.14 5.60 142.51 149.58 156.61 1685 1.00
## y_rep[40] 160.58 0.12 5.53 153.49 160.66 167.71 2018 1.00
## y_rep[41] 160.37 0.13 5.55 153.25 160.41 167.46 1926 1.00
## y_rep[42] 160.48 0.12 5.38 153.42 160.40 167.47 1916 1.00
## y_rep[43] 149.66 0.13 5.55 142.51 149.63 156.75 1833 1.00
## y_rep[44] 149.57 0.13 5.68 142.20 149.54 156.77 1817 1.00
## y_rep[45] 149.33 0.12 5.38 142.52 149.45 155.96 1864 1.00
## y_rep[46] 149.64 0.13 5.66 142.35 149.61 156.93 1830 1.00
## y_rep[47] 160.50 0.12 5.49 153.72 160.44 167.59 1938 1.00
## y_rep[48] 149.32 0.13 5.69 141.86 149.55 156.35 1958 1.00
## y_rep[49] 160.26 0.12 5.55 153.18 160.23 167.47 1985 1.00
## y_rep[50] 149.32 0.13 5.74 141.80 149.46 156.50 1956 1.00
## y_rep[51] 149.71 0.13 5.69 142.09 149.75 157.09 1797 1.00
## y_rep[52] 149.59 0.13 5.65 142.36 149.60 156.97 2029 1.00
## y_rep[53] 160.39 0.13 5.71 153.34 160.22 167.94 1829 1.00
## y_rep[54] 160.17 0.12 5.41 153.07 160.16 167.10 2165 1.00
## y_rep[55] 149.54 0.13 5.51 142.51 149.68 156.39 1906 1.00
## y_rep[56] 160.35 0.13 5.70 152.96 160.27 167.74 1840 1.00
## y_rep[57] 149.41 0.13 5.63 142.26 149.36 156.66 1891 1.00
## y_rep[58] 160.37 0.12 5.54 153.09 160.27 167.63 1981 1.00
## y_rep[59] 149.49 0.13 5.68 142.22 149.64 156.76 1955 1.00
## y_rep[60] 160.17 0.13 5.56 153.09 160.22 167.28 1903 1.00
## y_rep[61] 149.42 0.13 5.72 142.15 149.44 156.61 1933 1.00
## y_rep[62] 149.73 0.12 5.59 142.63 149.68 156.85 2122 1.00
## y_rep[63] 160.33 0.12 5.62 153.02 160.36 167.50 2094 1.00
## y_rep[64] 160.20 0.13 5.59 153.24 160.23 167.36 1721 1.00
## y_rep[65] 149.51 0.13 5.73 142.16 149.47 156.73 2035 1.00
## y_rep[66] 160.32 0.12 5.72 152.97 160.42 167.45 2127 1.00
## y_rep[67] 149.70 0.12 5.66 142.54 149.74 156.84 2057 1.00
## y_rep[68] 149.59 0.12 5.58 142.56 149.52 156.80 2084 1.00
## y_rep[69] 160.47 0.12 5.51 153.11 160.52 167.41 2087 1.00
## y_rep[70] 149.48 0.13 5.62 142.46 149.45 156.36 1779 1.00
## y_rep[71] 160.34 0.13 5.77 153.13 160.17 167.84 1979 1.00
## y_rep[72] 160.31 0.12 5.41 153.38 160.30 167.35 1894 1.00
## y_rep[73] 160.30 0.13 5.60 153.15 160.24 167.44 1877 1.00
## y_rep[74] 149.63 0.12 5.59 142.48 149.60 156.74 2086 1.00
## y_rep[75] 149.69 0.13 5.53 142.52 149.60 156.67 1751 1.00
## y_rep[76] 149.51 0.13 5.54 142.42 149.34 156.72 1777 1.00
## y_rep[77] 149.44 0.13 5.52 142.21 149.41 156.48 1836 1.00
## y_rep[78] 160.50 0.13 5.54 153.40 160.60 167.59 1895 1.00
## y_rep[79] 149.62 0.13 5.54 142.65 149.56 156.80 1842 1.00
## y_rep[80] 149.48 0.12 5.40 142.44 149.41 156.33 1902 1.00
## y_rep[81] 160.20 0.13 5.73 152.98 160.22 167.57 2032 1.00
## y_rep[82] 160.35 0.13 5.62 153.05 160.23 167.29 1917 1.00
## y_rep[83] 149.48 0.13 5.57 142.45 149.45 156.72 1823 1.00
## y_rep[84] 160.44 0.13 5.33 153.71 160.37 167.38 1680 1.00
## y_rep[85] 149.53 0.13 5.55 142.53 149.46 156.59 1943 1.00
## y_rep[86] 160.29 0.12 5.43 153.49 160.18 167.32 2228 1.00
## y_rep[87] 149.49 0.13 5.67 142.11 149.65 156.89 1861 1.00
## y_rep[88] 160.48 0.13 5.56 153.30 160.37 167.72 1710 1.00
## y_rep[89] 149.50 0.13 5.74 142.15 149.49 156.73 2027 1.00
## y_rep[90] 160.41 0.13 5.61 153.21 160.25 167.51 1996 1.00
## y_rep[91] 160.51 0.12 5.45 153.35 160.56 167.56 1966 1.00
## y_rep[92] 160.14 0.13 5.74 152.76 160.05 167.47 2019 1.00
## y_rep[93] 149.67 0.12 5.60 142.07 149.80 156.93 2110 1.00
## y_rep[94] 149.52 0.13 5.63 142.23 149.52 156.58 1921 1.00
## y_rep[95] 160.02 0.12 5.74 152.67 160.03 167.10 2167 1.00
## y_rep[96] 160.14 0.13 5.66 152.93 160.04 167.31 2043 1.00
## y_rep[97] 149.48 0.12 5.37 142.60 149.34 156.34 1972 1.00
## y_rep[98] 160.61 0.13 5.52 153.62 160.64 167.74 1815 1.00
## y_rep[99] 160.44 0.12 5.49 153.35 160.45 167.39 2061 1.00
## y_rep[100] 149.80 0.14 5.55 142.94 149.65 157.20 1660 1.00
## y_rep[101] 160.28 0.13 5.66 153.05 160.26 167.56 2036 1.00
## y_rep[102] 149.60 0.14 5.69 142.36 149.51 157.03 1756 1.00
## y_rep[103] 149.36 0.12 5.68 141.94 149.50 156.57 2074 1.00
## y_rep[104] 160.41 0.13 5.56 153.21 160.24 167.65 1804 1.00
## y_rep[105] 160.34 0.12 5.67 153.02 160.38 167.49 2072 1.00
## y_rep[106] 149.66 0.14 5.77 142.41 149.69 157.17 1705 1.00
## y_rep[107] 149.47 0.13 5.47 142.47 149.45 156.46 1831 1.00
## y_rep[108] 149.29 0.13 5.59 142.11 149.36 156.29 1816 1.00
## y_rep[109] 160.46 0.13 5.70 153.04 160.59 167.84 1951 1.00
## y_rep[110] 149.64 0.13 5.72 142.31 149.54 156.94 1970 1.00
## y_rep[111] 160.45 0.13 5.46 153.61 160.44 167.45 1710 1.00
## y_rep[112] 149.56 0.13 5.71 142.09 149.34 157.17 1889 1.00
## y_rep[113] 149.66 0.13 5.71 142.47 149.81 156.67 2024 1.00
## y_rep[114] 160.42 0.13 5.73 153.36 160.31 167.83 1898 1.00
## y_rep[115] 160.43 0.13 5.50 153.76 160.34 167.53 1678 1.00
## y_rep[116] 149.45 0.13 5.55 142.29 149.50 156.52 1960 1.00
## y_rep[117] 160.27 0.12 5.44 153.30 160.17 167.23 1977 1.00
## y_rep[118] 160.34 0.12 5.61 153.18 160.26 167.57 2080 1.00
## y_rep[119] 149.77 0.13 5.57 142.65 149.69 156.98 1858 1.00
## y_rep[120] 149.57 0.12 5.60 142.46 149.46 156.75 2048 1.00
## y_rep[121] 160.24 0.13 5.83 152.81 160.16 167.53 1868 1.00
## y_rep[122] 149.55 0.13 5.66 142.39 149.58 156.48 2049 1.00
## y_rep[123] 160.16 0.13 5.64 152.80 160.23 167.39 1887 1.00
## y_rep[124] 149.64 0.12 5.60 142.60 149.58 156.73 2087 1.00
## y_rep[125] 149.54 0.12 5.58 142.37 149.66 156.71 2018 1.00
## y_rep[126] 149.65 0.13 5.51 142.46 149.66 156.42 1719 1.00
## y_rep[127] 149.69 0.13 5.61 142.59 149.77 156.50 1879 1.00
## y_rep[128] 160.36 0.13 5.54 153.24 160.30 167.64 1930 1.00
## y_rep[129] 149.60 0.12 5.53 142.50 149.65 156.86 1970 1.00
## y_rep[130] 149.56 0.14 5.49 142.53 149.60 156.55 1646 1.00
## y_rep[131] 160.21 0.13 5.59 152.87 160.29 167.29 1880 1.00
## y_rep[132] 160.37 0.14 5.66 153.09 160.48 167.66 1726 1.00
## y_rep[133] 149.32 0.13 5.57 142.29 149.29 156.63 1843 1.00
## y_rep[134] 160.46 0.12 5.63 153.12 160.52 167.76 2033 1.00
## y_rep[135] 149.49 0.13 5.63 142.33 149.50 156.57 1984 1.00
## y_rep[136] 160.51 0.12 5.69 153.18 160.62 167.75 2216 1.00
## y_rep[137] 160.58 0.14 5.63 153.35 160.63 167.90 1695 1.00
## y_rep[138] 160.27 0.13 5.55 153.16 160.20 167.30 1930 1.00
## y_rep[139] 149.63 0.12 5.47 142.67 149.67 156.71 2040 1.00
## y_rep[140] 160.52 0.12 5.41 153.67 160.49 167.49 1928 1.00
## y_rep[141] 149.41 0.13 5.66 142.49 149.37 156.64 1946 1.00
## y_rep[142] 149.43 0.12 5.47 142.24 149.58 156.42 1934 1.00
## y_rep[143] 149.50 0.12 5.50 142.60 149.42 156.71 1988 1.00
## y_rep[144] 149.55 0.13 5.72 142.21 149.63 156.85 1969 1.00
## y_rep[145] 149.53 0.12 5.55 142.55 149.43 156.92 2303 1.00
## y_rep[146] 160.50 0.13 5.67 153.20 160.58 167.66 1940 1.00
## y_rep[147] 149.68 0.12 5.45 142.66 149.52 157.05 1950 1.00
## y_rep[148] 149.56 0.13 5.72 142.39 149.41 157.01 2042 1.00
## y_rep[149] 160.24 0.13 5.51 153.26 160.34 167.17 1698 1.00
## y_rep[150] 149.39 0.13 5.71 142.22 149.29 156.58 1976 1.00
## y_rep[151] 160.46 0.13 5.59 153.36 160.58 167.50 1974 1.00
## y_rep[152] 149.61 0.13 5.58 142.26 149.68 156.76 1978 1.00
## y_rep[153] 160.21 0.13 5.63 152.95 160.35 167.43 1873 1.00
## y_rep[154] 149.62 0.12 5.57 142.38 149.68 156.64 1989 1.00
## y_rep[155] 160.28 0.12 5.45 153.35 160.40 167.45 2055 1.00
## y_rep[156] 149.45 0.12 5.57 142.39 149.53 156.51 2016 1.00
## y_rep[157] 149.47 0.12 5.50 142.49 149.49 156.55 2139 1.00
## y_rep[158] 160.43 0.13 5.57 153.32 160.48 167.40 1901 1.00
## y_rep[159] 160.43 0.12 5.67 153.14 160.55 167.35 2095 1.00
## y_rep[160] 149.51 0.13 5.68 142.26 149.40 156.75 1842 1.00
## y_rep[161] 160.45 0.13 5.60 153.35 160.36 167.69 1929 1.00
## y_rep[162] 149.31 0.12 5.48 142.24 149.41 156.27 2108 1.00
## y_rep[163] 160.30 0.12 5.50 153.21 160.12 167.49 2048 1.00
## y_rep[164] 160.35 0.13 5.54 153.24 160.15 167.42 1811 1.00
## y_rep[165] 160.32 0.13 5.57 153.09 160.45 167.55 1890 1.00
## y_rep[166] 149.36 0.13 5.50 142.28 149.40 156.54 1801 1.00
## y_rep[167] 160.34 0.13 5.54 153.48 160.26 167.48 1929 1.00
## y_rep[168] 149.72 0.13 5.57 142.52 149.87 156.57 1929 1.00
## y_rep[169] 149.36 0.13 5.58 141.93 149.48 156.48 1890 1.00
## y_rep[170] 149.55 0.12 5.40 142.57 149.46 156.41 2029 1.00
## y_rep[171] 149.51 0.12 5.39 142.66 149.33 156.52 1964 1.00
## y_rep[172] 160.28 0.13 5.58 153.06 160.27 167.36 1824 1.00
## y_rep[173] 149.64 0.13 5.64 142.51 149.54 156.62 1976 1.00
## y_rep[174] 160.43 0.13 5.69 153.26 160.47 167.92 1912 1.00
## y_rep[175] 149.33 0.12 5.49 142.04 149.34 156.40 2021 1.00
## y_rep[176] 160.26 0.12 5.41 153.26 160.34 167.09 1924 1.00
## y_rep[177] 149.59 0.13 5.57 142.68 149.52 156.66 1729 1.00
## y_rep[178] 149.64 0.13 5.54 142.46 149.56 156.66 1865 1.00
## y_rep[179] 160.38 0.12 5.51 153.22 160.34 167.35 2049 1.00
## y_rep[180] 149.54 0.12 5.63 142.37 149.53 156.71 2122 1.00
## y_rep[181] 160.05 0.12 5.51 152.93 160.15 167.06 1988 1.00
## y_rep[182] 149.39 0.12 5.60 142.12 149.55 156.54 2011 1.00
## y_rep[183] 149.49 0.13 5.58 142.44 149.51 156.82 1918 1.00
## y_rep[184] 149.44 0.13 5.55 142.50 149.44 156.51 1883 1.00
## y_rep[185] 160.34 0.12 5.55 153.20 160.27 167.28 2027 1.00
## y_rep[186] 160.68 0.13 5.68 153.55 160.72 168.02 1975 1.00
## y_rep[187] 149.32 0.12 5.53 142.30 149.35 156.41 2096 1.00
## y_rep[188] 160.41 0.12 5.46 153.20 160.62 167.16 2161 1.00
## y_rep[189] 149.56 0.13 5.61 142.44 149.41 156.91 1957 1.00
## y_rep[190] 160.31 0.13 5.59 153.17 160.44 167.22 1995 1.00
## y_rep[191] 149.33 0.13 5.66 142.05 149.41 156.53 1801 1.00
## y_rep[192] 160.30 0.12 5.49 153.20 160.29 167.31 1936 1.00
## y_rep[193] 149.46 0.12 5.56 142.57 149.44 156.55 2009 1.00
## y_rep[194] 160.37 0.12 5.58 153.07 160.49 167.52 2092 1.00
## y_rep[195] 149.64 0.13 5.62 142.69 149.47 156.77 1945 1.00
## y_rep[196] 149.62 0.12 5.52 142.55 149.62 156.75 1999 1.00
## y_rep[197] 149.41 0.13 5.52 142.17 149.48 156.27 1747 1.00
## y_rep[198] 160.37 0.13 5.58 153.24 160.31 167.84 1955 1.00
## y_rep[199] 160.34 0.14 5.50 153.35 160.45 167.32 1554 1.00
## y_rep[200] 149.73 0.13 5.72 142.88 149.66 157.15 1967 1.00
## y_rep[201] 160.63 0.12 5.64 153.37 160.69 167.74 2059 1.00
## y_rep[202] 149.26 0.12 5.53 142.25 149.06 156.55 1976 1.00
## y_rep[203] 160.38 0.12 5.61 153.21 160.33 167.45 2046 1.00
## y_rep[204] 149.49 0.12 5.50 142.51 149.60 156.28 2011 1.00
## y_rep[205] 160.29 0.12 5.43 153.34 160.28 167.11 1897 1.00
## y_rep[206] 149.49 0.13 5.63 142.15 149.52 156.64 1899 1.00
## y_rep[207] 149.57 0.13 5.54 142.31 149.71 156.63 1944 1.00
## y_rep[208] 149.59 0.14 5.63 142.44 149.64 156.68 1731 1.00
## y_rep[209] 149.35 0.12 5.51 142.09 149.34 156.35 2127 1.00
## y_rep[210] 149.37 0.13 5.54 142.13 149.44 156.40 1731 1.00
## y_rep[211] 160.27 0.13 5.48 153.25 160.26 167.24 1914 1.00
## y_rep[212] 160.31 0.12 5.47 153.39 160.35 167.26 1935 1.00
## y_rep[213] 160.25 0.13 5.67 153.00 160.28 167.48 2011 1.00
## y_rep[214] 149.50 0.12 5.53 142.38 149.38 156.67 2100 1.00
## y_rep[215] 160.12 0.12 5.56 152.67 160.26 167.06 2014 1.00
## y_rep[216] 160.37 0.13 5.57 153.23 160.45 167.54 1881 1.00
## y_rep[217] 160.35 0.14 5.63 153.07 160.30 167.51 1550 1.00
## y_rep[218] 149.38 0.13 5.61 142.15 149.44 156.52 1981 1.00
## y_rep[219] 160.61 0.13 5.54 153.55 160.52 167.71 1836 1.00
## y_rep[220] 149.47 0.13 5.63 142.08 149.53 156.49 1929 1.00
## y_rep[221] 149.44 0.13 5.72 142.11 149.48 156.68 2020 1.00
## y_rep[222] 149.50 0.12 5.47 142.47 149.33 156.69 1979 1.00
## y_rep[223] 160.27 0.13 5.64 153.15 160.22 167.44 2012 1.00
## y_rep[224] 149.57 0.13 5.67 142.54 149.55 156.93 2032 1.00
## y_rep[225] 160.32 0.14 5.64 153.12 160.26 167.79 1728 1.00
## y_rep[226] 149.53 0.12 5.59 142.33 149.59 156.61 2058 1.00
## y_rep[227] 149.46 0.13 5.64 142.02 149.46 156.80 2012 1.00
## y_rep[228] 160.53 0.12 5.68 153.40 160.28 168.06 2105 1.00
## y_rep[229] 149.70 0.13 5.46 142.84 149.62 156.88 1895 1.00
## y_rep[230] 160.35 0.13 5.60 153.23 160.32 167.45 1975 1.00
## y_rep[231] 160.50 0.12 5.44 153.53 160.43 167.60 1930 1.00
## y_rep[232] 149.69 0.13 5.70 142.33 149.73 157.02 1953 1.00
## y_rep[233] 149.40 0.13 5.47 142.41 149.39 156.53 1856 1.00
## y_rep[234] 160.39 0.12 5.60 153.14 160.38 167.34 2042 1.00
## y_rep[235] 160.52 0.12 5.54 153.83 160.22 167.78 2190 1.00
## y_rep[236] 149.38 0.13 5.63 141.93 149.43 156.72 1786 1.00
## y_rep[237] 160.39 0.12 5.46 153.32 160.43 167.40 2009 1.00
## y_rep[238] 149.84 0.12 5.43 142.82 149.70 156.82 2161 1.00
## y_rep[239] 149.62 0.12 5.56 142.56 149.59 156.98 2014 1.00
## y_rep[240] 149.46 0.14 5.57 142.12 149.58 156.35 1532 1.00
## y_rep[241] 149.61 0.13 5.68 142.30 149.65 157.13 1929 1.00
## y_rep[242] 160.24 0.13 5.67 153.00 160.36 167.45 1932 1.00
## y_rep[243] 160.41 0.12 5.66 153.28 160.37 167.69 2084 1.00
## y_rep[244] 149.48 0.12 5.56 142.25 149.37 156.51 1996 1.00
## y_rep[245] 160.44 0.13 5.67 153.27 160.50 167.80 1763 1.00
## y_rep[246] 149.45 0.13 5.50 142.61 149.42 156.49 1748 1.00
## y_rep[247] 160.44 0.13 5.67 153.30 160.44 167.68 1818 1.00
## y_rep[248] 149.55 0.13 5.55 142.60 149.43 156.65 1961 1.00
## y_rep[249] 160.54 0.13 5.55 153.44 160.50 167.62 1846 1.00
## y_rep[250] 160.30 0.12 5.63 153.15 160.27 167.74 2212 1.00
## y_rep[251] 160.28 0.13 5.55 153.21 160.37 167.15 1856 1.00
## y_rep[252] 160.29 0.13 5.70 152.94 160.36 167.72 1932 1.00
## y_rep[253] 149.54 0.14 5.70 142.34 149.43 156.73 1678 1.00
## y_rep[254] 149.66 0.12 5.64 142.36 149.77 156.70 2082 1.00
## y_rep[255] 149.63 0.13 5.65 142.27 149.67 156.88 1978 1.00
## y_rep[256] 149.44 0.13 5.60 142.40 149.42 156.62 1936 1.00
## y_rep[257] 160.44 0.13 5.56 153.35 160.39 167.44 1965 1.00
## y_rep[258] 149.59 0.12 5.55 142.71 149.48 156.53 2135 1.00
## y_rep[259] 160.41 0.13 5.47 153.40 160.48 167.48 1775 1.00
## y_rep[260] 160.25 0.13 5.65 153.05 160.15 167.56 1857 1.00
## y_rep[261] 160.22 0.12 5.48 153.43 160.16 167.19 1943 1.00
## y_rep[262] 149.71 0.12 5.67 142.44 149.69 156.91 2074 1.00
## y_rep[263] 149.51 0.13 5.56 142.59 149.49 156.56 1780 1.00
## y_rep[264] 149.62 0.13 5.77 142.30 149.71 156.87 2042 1.00
## y_rep[265] 160.49 0.13 5.60 153.33 160.39 167.69 1945 1.00
## y_rep[266] 149.54 0.13 5.48 142.59 149.54 156.57 1768 1.00
## y_rep[267] 160.44 0.13 5.59 153.38 160.40 167.51 1955 1.00
## y_rep[268] 149.42 0.13 5.60 142.33 149.28 156.48 1935 1.00
## y_rep[269] 149.64 0.13 5.59 142.49 149.73 156.68 1958 1.00
## y_rep[270] 160.39 0.13 5.79 152.90 160.36 167.90 1900 1.00
## y_rep[271] 160.61 0.12 5.68 153.29 160.71 167.86 2077 1.00
## y_rep[272] 149.25 0.12 5.50 142.13 149.43 156.21 1934 1.00
## y_rep[273] 160.44 0.13 5.54 153.46 160.42 167.51 1928 1.00
## y_rep[274] 160.38 0.12 5.35 153.50 160.26 167.18 1985 1.00
## y_rep[275] 149.51 0.13 5.54 142.61 149.33 156.61 1837 1.00
## y_rep[276] 160.31 0.12 5.63 153.14 160.46 167.68 2105 1.00
## y_rep[277] 149.65 0.12 5.32 142.70 149.51 156.68 1978 1.00
## y_rep[278] 149.27 0.13 5.62 141.89 149.37 156.25 1980 1.00
## y_rep[279] 160.35 0.13 5.58 153.18 160.31 167.39 1913 1.00
## y_rep[280] 149.50 0.12 5.51 142.42 149.40 156.65 1994 1.00
## y_rep[281] 149.74 0.13 5.70 142.65 149.57 157.07 1924 1.00
## y_rep[282] 160.18 0.12 5.56 153.09 160.23 167.10 2043 1.00
## y_rep[283] 149.42 0.12 5.41 142.43 149.36 156.40 2059 1.00
## y_rep[284] 160.28 0.13 5.50 153.04 160.27 167.44 1908 1.00
## y_rep[285] 149.41 0.12 5.54 142.38 149.42 156.39 2139 1.00
## y_rep[286] 160.32 0.12 5.54 153.17 160.38 167.22 2016 1.00
## y_rep[287] 160.53 0.13 5.58 153.31 160.60 167.73 1937 1.00
## y_rep[288] 160.40 0.12 5.65 153.00 160.71 167.66 2159 1.00
## y_rep[289] 149.58 0.13 5.66 142.40 149.56 156.86 2035 1.00
## y_rep[290] 160.37 0.13 5.63 152.99 160.38 167.36 1925 1.00
## y_rep[291] 160.29 0.12 5.51 153.39 160.02 167.33 1998 1.00
## y_rep[292] 160.21 0.13 5.54 153.07 160.22 167.27 1808 1.00
## y_rep[293] 160.38 0.12 5.41 153.43 160.47 167.07 2015 1.00
## y_rep[294] 149.62 0.12 5.45 142.65 149.63 156.70 2122 1.00
## y_rep[295] 160.25 0.13 5.62 153.02 160.31 167.14 2016 1.00
## y_rep[296] 149.61 0.13 5.64 142.29 149.65 156.71 1987 1.00
## y_rep[297] 149.60 0.13 5.55 142.47 149.70 156.85 1736 1.00
## y_rep[298] 149.53 0.12 5.50 142.52 149.57 156.72 2110 1.00
## y_rep[299] 160.47 0.12 5.49 153.36 160.34 167.58 2077 1.00
## y_rep[300] 160.25 0.13 5.52 153.06 160.35 167.44 1738 1.00
## y_rep[301] 149.42 0.13 5.50 142.63 149.33 156.52 1866 1.00
## y_rep[302] 160.53 0.12 5.70 153.06 160.65 167.63 2208 1.00
## y_rep[303] 149.64 0.12 5.57 142.35 149.72 156.83 2070 1.00
## y_rep[304] 160.54 0.12 5.46 153.63 160.35 167.64 2003 1.00
## y_rep[305] 160.23 0.12 5.61 152.92 160.26 167.51 2065 1.00
## y_rep[306] 160.34 0.12 5.50 153.26 160.45 167.14 2165 1.00
## y_rep[307] 160.48 0.12 5.66 153.20 160.35 167.90 2114 1.00
## y_rep[308] 149.48 0.13 5.65 142.28 149.54 156.84 2029 1.00
## y_rep[309] 149.61 0.13 5.54 142.29 149.59 156.70 1849 1.00
## y_rep[310] 149.54 0.12 5.48 142.48 149.54 156.54 2041 1.00
## y_rep[311] 149.67 0.12 5.71 142.32 149.77 156.93 2134 1.00
## y_rep[312] 149.52 0.13 5.41 142.64 149.40 156.38 1726 1.00
## y_rep[313] 160.33 0.13 5.64 153.13 160.17 167.77 1948 1.00
## y_rep[314] 149.36 0.13 5.46 142.53 149.30 156.38 1885 1.00
## y_rep[315] 160.07 0.12 5.53 152.91 160.09 167.38 2002 1.00
## y_rep[316] 149.48 0.13 5.65 142.31 149.45 156.77 1925 1.00
## y_rep[317] 160.40 0.12 5.59 153.21 160.37 167.46 2003 1.00
## y_rep[318] 149.38 0.13 5.56 142.47 149.23 156.37 1912 1.00
## y_rep[319] 160.33 0.13 5.68 153.23 160.20 167.69 1971 1.00
## y_rep[320] 149.50 0.12 5.52 142.47 149.43 156.71 2005 1.00
## y_rep[321] 160.47 0.12 5.65 153.20 160.54 167.71 2102 1.00
## y_rep[322] 149.40 0.12 5.50 142.52 149.32 156.41 2026 1.00
## y_rep[323] 160.50 0.13 5.49 153.42 160.50 167.55 1925 1.00
## y_rep[324] 160.61 0.13 5.62 153.26 160.55 167.99 1884 1.00
## y_rep[325] 149.57 0.13 5.72 142.30 149.50 156.83 2018 1.00
## y_rep[326] 149.46 0.12 5.67 142.39 149.45 156.78 2207 1.00
## y_rep[327] 149.41 0.13 5.61 142.19 149.50 156.42 1912 1.00
## y_rep[328] 160.34 0.13 5.73 152.92 160.24 167.55 1829 1.00
## y_rep[329] 160.45 0.13 5.57 153.58 160.21 167.69 1821 1.00
## y_rep[330] 160.66 0.13 5.67 153.28 160.62 167.78 1887 1.00
## y_rep[331] 160.33 0.12 5.72 152.86 160.33 167.53 2119 1.00
## y_rep[332] 160.66 0.12 5.49 153.64 160.54 167.72 2024 1.00
## y_rep[333] 149.51 0.13 5.67 142.50 149.65 156.75 1852 1.00
## y_rep[334] 160.45 0.13 5.58 153.32 160.46 167.98 1901 1.00
## y_rep[335] 149.57 0.13 5.60 142.47 149.58 156.91 1957 1.00
## y_rep[336] 160.35 0.12 5.63 153.16 160.44 167.40 2029 1.00
## y_rep[337] 149.53 0.13 5.70 142.30 149.49 156.75 2008 1.00
## y_rep[338] 149.52 0.13 5.69 142.37 149.50 157.05 2005 1.00
## y_rep[339] 149.58 0.13 5.58 142.44 149.67 156.59 1994 1.00
## y_rep[340] 149.60 0.12 5.46 142.47 149.72 156.79 2034 1.00
## y_rep[341] 149.38 0.13 5.69 142.09 149.44 156.62 1998 1.00
## y_rep[342] 160.36 0.12 5.51 153.43 160.20 167.39 2073 1.00
## y_rep[343] 149.52 0.12 5.33 142.77 149.49 156.35 2045 1.00
## y_rep[344] 160.30 0.14 5.59 152.97 160.34 167.31 1572 1.00
## y_rep[345] 149.71 0.12 5.70 142.40 149.67 157.00 2088 1.00
## y_rep[346] 160.38 0.13 5.53 153.30 160.38 167.34 1849 1.00
## y_rep[347] 149.54 0.13 5.73 141.98 149.65 156.87 2018 1.00
## y_rep[348] 149.35 0.12 5.43 142.43 149.34 156.23 1929 1.00
## y_rep[349] 149.40 0.12 5.50 142.42 149.44 156.39 1983 1.00
## y_rep[350] 160.29 0.12 5.59 153.18 160.31 167.50 2061 1.00
## y_rep[351] 149.53 0.14 5.55 142.44 149.48 156.40 1688 1.00
## y_rep[352] 160.32 0.13 5.54 153.22 160.23 167.28 1943 1.00
## lp__ -780.54 0.06 1.23 -782.17 -780.23 -779.32 423 1.02
##
## Samples were drawn using NUTS(diag_e) at Fri Nov 22 15:25:38 2019.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).summary(lm(height~as.factor(male),data=howell2))##
## Call:
## lm(formula = height ~ as.factor(male), data = howell2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -20.6585 -3.4635 0.2965 3.4715 18.7115
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 149.5135 0.4049 369.25 <2e-16 ***
## as.factor(male)1 10.8450 0.5914 18.34 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.537 on 350 degrees of freedom
## Multiple R-squared: 0.49, Adjusted R-squared: 0.4885
## F-statistic: 336.3 on 1 and 350 DF, p-value: < 2.2e-16Convergence diagnostics
posterior <- as.array(fit.m5_1_1) # posterior draws
lp <- log_posterior(fit.m5_1_1) # log of the posterior density for each draw
np <- nuts_params(fit.m5_1_1) # Some NUTS-specific diagnostic values
mcmc_parcoord(posterior, np = np,pars=c("beta[1]","beta[2]","sigma")) 
mcmc_pairs(posterior, np = np, pars = c("beta[1]","beta[2]","sigma"), off_diag_args = list(size = 0.75)) # Pairs plots
mcmc_trace(posterior, pars = c("beta[1]","beta[2]","sigma"), np = np) + xlab("Post-warmup iteration") # Trace plots## No divergences to plot.
Same outputs with another prior for sigma: \(\sigma \sim \, {\rm Cauchy} (0,5)\)
data {
int<lower=0> N; // number of observations
int<lower=0> n; // number of levels of the categorical variable
vector[N] height; // response variables
matrix[N,n] X; // categorical variable
}
parameters {
vector[n] beta; // intercepts of the categorical variable
real sigma;
}
transformed parameters {
vector[N] mu;
mu = X*beta;
}
model {
height ~ normal(mu ,sigma); // likelihood
sigma ~ cauchy(0,5);
beta[1] ~ normal(178,20);
beta[2] ~ normal(0,10);
// beta ~ normal(0,1000)
}
generated quantities {
vector[N] y_rep;
for(i in 1:N)
y_rep[i] = normal_rng(mu[i], sigma);
}
fit.m5_1_2 <- sampling(m5.1.2, data = m5.1.data, iter = 1000, chains = 4, cores = 4)
print(fit.m5_1_2, probs = c(0.10, 0.5, 0.9))## Inference for Stan model: 4c192013905ef0bcb3999ba4bc93cd6e.
## 4 chains, each with iter=1000; warmup=500; thin=1;
## post-warmup draws per chain=500, total post-warmup draws=2000.
##
## mean se_mean sd 10% 50% 90% n_eff Rhat
## beta[1] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## beta[2] 10.79 0.02 0.58 10.03 10.81 11.52 1353 1.00
## sigma 5.55 0.01 0.21 5.29 5.54 5.84 1382 1.00
## mu[1] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[2] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[3] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[4] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[5] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[6] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[7] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[8] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[9] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[10] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[11] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[12] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[13] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[14] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[15] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[16] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[17] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[18] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[19] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[20] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[21] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[22] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[23] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[24] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[25] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[26] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[27] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[28] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[29] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[30] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[31] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[32] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[33] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[34] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[35] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[36] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[37] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[38] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[39] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[40] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[41] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[42] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[43] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[44] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[45] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[46] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[47] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[48] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[49] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[50] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[51] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[52] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[53] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[54] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[55] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[56] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[57] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[58] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[59] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[60] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[61] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[62] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[63] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[64] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[65] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[66] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[67] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[68] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[69] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[70] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[71] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[72] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[73] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[74] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[75] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[76] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[77] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[78] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[79] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[80] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[81] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[82] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[83] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[84] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[85] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[86] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[87] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[88] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[89] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[90] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[91] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[92] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[93] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[94] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[95] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[96] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[97] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[98] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[99] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[100] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[101] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[102] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[103] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[104] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[105] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[106] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[107] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[108] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[109] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[110] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[111] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[112] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[113] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[114] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[115] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[116] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[117] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[118] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[119] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[120] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[121] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[122] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[123] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[124] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[125] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[126] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[127] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[128] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[129] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[130] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[131] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[132] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[133] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[134] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[135] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[136] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[137] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[138] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[139] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[140] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[141] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[142] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[143] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[144] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[145] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[146] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[147] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[148] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[149] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[150] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[151] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[152] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[153] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[154] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[155] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[156] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[157] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[158] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[159] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[160] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[161] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[162] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[163] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[164] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[165] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[166] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[167] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[168] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[169] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[170] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[171] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[172] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[173] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[174] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[175] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[176] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[177] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[178] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[179] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[180] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[181] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[182] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[183] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[184] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[185] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[186] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[187] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[188] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[189] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[190] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[191] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[192] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[193] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[194] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[195] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[196] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[197] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[198] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[199] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[200] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[201] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[202] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[203] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[204] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[205] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[206] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[207] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[208] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[209] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[210] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[211] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[212] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[213] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[214] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[215] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[216] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[217] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[218] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[219] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[220] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[221] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[222] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[223] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[224] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[225] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[226] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[227] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[228] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[229] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[230] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[231] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[232] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[233] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[234] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[235] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[236] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[237] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[238] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[239] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[240] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[241] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[242] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[243] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[244] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[245] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[246] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[247] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[248] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[249] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[250] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[251] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[252] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[253] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[254] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[255] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[256] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[257] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[258] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[259] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[260] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[261] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[262] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[263] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[264] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[265] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[266] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[267] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[268] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[269] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[270] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[271] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[272] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[273] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[274] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[275] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[276] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[277] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[278] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[279] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[280] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[281] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[282] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[283] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[284] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[285] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[286] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[287] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[288] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[289] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[290] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[291] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[292] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[293] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[294] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[295] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[296] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[297] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[298] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[299] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[300] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[301] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[302] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[303] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[304] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[305] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[306] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[307] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[308] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[309] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[310] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[311] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[312] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[313] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[314] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[315] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[316] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[317] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[318] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[319] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[320] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[321] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[322] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[323] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[324] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[325] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[326] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[327] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[328] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[329] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[330] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[331] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[332] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[333] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[334] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[335] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[336] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[337] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[338] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[339] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[340] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[341] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[342] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[343] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[344] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[345] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[346] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[347] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[348] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[349] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[350] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## mu[351] 149.54 0.01 0.40 149.03 149.55 150.06 1320 1.00
## mu[352] 160.34 0.01 0.43 159.80 160.34 160.88 2106 1.00
## y_rep[1] 160.43 0.13 5.78 153.05 160.49 167.64 1948 1.00
## y_rep[2] 149.69 0.12 5.33 142.86 149.59 156.64 1974 1.00
## y_rep[3] 149.59 0.13 5.81 142.13 149.72 156.97 2072 1.00
## y_rep[4] 160.20 0.15 5.74 152.95 160.13 167.60 1546 1.00
## y_rep[5] 149.47 0.12 5.45 142.47 149.41 156.55 2029 1.00
## y_rep[6] 160.42 0.12 5.55 153.17 160.43 167.55 2041 1.00
## y_rep[7] 149.77 0.13 5.52 142.87 149.73 156.70 1791 1.00
## y_rep[8] 160.31 0.14 5.61 153.08 160.32 167.64 1727 1.00
## y_rep[9] 149.32 0.12 5.65 141.86 149.37 156.49 2053 1.00
## y_rep[10] 160.42 0.12 5.42 153.51 160.27 167.49 1957 1.00
## y_rep[11] 149.60 0.13 5.52 142.54 149.53 156.64 1763 1.00
## y_rep[12] 160.39 0.13 5.66 153.03 160.52 167.66 1986 1.00
## y_rep[13] 149.67 0.14 5.51 142.72 149.63 156.79 1648 1.00
## y_rep[14] 149.76 0.13 5.62 142.61 149.48 157.15 1841 1.00
## y_rep[15] 149.59 0.12 5.47 142.49 149.50 156.37 1943 1.00
## y_rep[16] 160.25 0.12 5.60 153.10 160.26 167.33 2149 1.00
## y_rep[17] 160.51 0.13 5.66 153.08 160.53 167.74 2051 1.00
## y_rep[18] 149.77 0.13 5.60 142.74 149.77 156.98 1995 1.00
## y_rep[19] 160.12 0.12 5.58 153.08 160.07 167.34 2020 1.00
## y_rep[20] 149.64 0.12 5.47 142.84 149.59 156.65 1947 1.00
## y_rep[21] 160.52 0.12 5.72 152.95 160.45 168.10 2110 1.00
## y_rep[22] 149.64 0.13 5.64 142.55 149.39 156.82 1770 1.00
## y_rep[23] 149.60 0.13 5.67 142.45 149.50 156.62 2044 1.00
## y_rep[24] 160.13 0.12 5.68 152.79 160.13 167.26 2136 1.00
## y_rep[25] 160.48 0.13 5.64 153.08 160.67 167.60 2006 1.00
## y_rep[26] 149.42 0.13 5.59 142.22 149.53 156.56 1938 1.00
## y_rep[27] 149.60 0.12 5.63 142.29 149.68 156.73 2028 1.00
## y_rep[28] 149.50 0.13 5.65 142.32 149.62 156.96 1853 1.00
## y_rep[29] 149.43 0.12 5.43 142.27 149.41 156.38 1938 1.00
## y_rep[30] 149.72 0.13 5.46 142.69 149.68 156.71 1799 1.00
## y_rep[31] 149.54 0.12 5.47 142.45 149.67 156.27 1953 1.00
## y_rep[32] 160.37 0.13 5.50 153.20 160.38 167.46 1924 1.00
## y_rep[33] 160.20 0.13 5.71 152.81 160.10 167.48 1950 1.00
## y_rep[34] 160.28 0.13 5.66 153.05 160.17 167.57 2001 1.00
## y_rep[35] 160.29 0.12 5.43 153.39 160.20 167.11 1951 1.00
## y_rep[36] 149.57 0.12 5.51 142.68 149.60 156.50 2042 1.00
## y_rep[37] 149.33 0.13 5.55 142.29 149.32 156.60 1829 1.00
## y_rep[38] 160.31 0.13 5.60 153.13 160.30 167.36 1852 1.00
## y_rep[39] 149.47 0.13 5.59 142.27 149.27 156.77 1871 1.00
## y_rep[40] 160.25 0.12 5.63 153.25 160.23 167.28 2036 1.00
## y_rep[41] 160.10 0.12 5.64 152.98 160.14 167.36 2130 1.00
## y_rep[42] 160.42 0.12 5.39 153.40 160.57 167.11 1947 1.00
## y_rep[43] 149.53 0.15 5.63 142.35 149.51 156.61 1451 1.00
## y_rep[44] 149.52 0.13 5.52 142.73 149.64 156.30 1930 1.00
## y_rep[45] 149.71 0.13 5.70 142.50 149.78 157.06 2061 1.00
## y_rep[46] 149.34 0.12 5.50 142.21 149.39 156.18 1979 1.00
## y_rep[47] 160.47 0.13 5.47 153.52 160.45 167.43 1913 1.00
## y_rep[48] 149.58 0.12 5.44 142.91 149.60 156.72 2051 1.00
## y_rep[49] 160.37 0.12 5.70 152.99 160.37 167.88 2180 1.00
## y_rep[50] 149.58 0.13 5.67 142.34 149.68 156.57 2008 1.00
## y_rep[51] 149.14 0.13 5.64 141.86 149.26 156.45 1956 1.00
## y_rep[52] 149.78 0.13 5.68 142.25 149.88 157.02 1934 1.00
## y_rep[53] 160.31 0.12 5.60 153.29 160.23 167.65 2185 1.00
## y_rep[54] 160.15 0.13 5.70 152.95 160.19 167.25 1919 1.00
## y_rep[55] 149.42 0.13 5.51 142.38 149.43 156.80 1917 1.00
## y_rep[56] 160.40 0.12 5.53 153.19 160.41 167.47 2002 1.00
## y_rep[57] 149.40 0.13 5.70 142.17 149.38 156.47 1983 1.00
## y_rep[58] 160.34 0.13 5.64 153.20 160.46 167.51 1932 1.00
## y_rep[59] 149.84 0.12 5.56 142.62 149.85 156.81 1995 1.00
## y_rep[60] 160.19 0.14 5.66 152.95 160.16 167.32 1711 1.00
## y_rep[61] 149.50 0.12 5.55 142.43 149.45 156.69 2011 1.00
## y_rep[62] 149.63 0.12 5.40 142.72 149.64 156.74 2123 1.00
## y_rep[63] 160.38 0.12 5.45 153.51 160.21 167.38 2043 1.00
## y_rep[64] 160.47 0.12 5.54 153.31 160.42 167.53 2059 1.00
## y_rep[65] 149.34 0.14 5.70 141.92 149.45 156.53 1732 1.00
## y_rep[66] 160.43 0.13 5.68 153.23 160.56 167.76 2012 1.00
## y_rep[67] 149.55 0.14 5.63 142.33 149.62 156.81 1625 1.00
## y_rep[68] 149.48 0.12 5.47 142.39 149.44 156.43 2003 1.00
## y_rep[69] 160.42 0.13 5.60 152.88 160.56 167.52 2005 1.00
## y_rep[70] 149.67 0.13 5.61 142.46 149.55 156.85 1862 1.00
## y_rep[71] 160.43 0.12 5.54 153.39 160.50 167.46 2097 1.00
## y_rep[72] 160.41 0.12 5.70 153.08 160.33 167.75 2082 1.00
## y_rep[73] 160.48 0.13 5.54 153.22 160.62 167.44 1928 1.00
## y_rep[74] 149.45 0.12 5.57 142.20 149.43 156.66 2073 1.00
## y_rep[75] 149.34 0.12 5.50 142.33 149.38 156.42 2011 1.00
## y_rep[76] 149.45 0.12 5.44 142.46 149.40 156.61 1914 1.00
## y_rep[77] 149.56 0.12 5.56 142.66 149.57 156.76 2132 1.00
## y_rep[78] 160.23 0.12 5.51 153.23 160.11 167.36 1950 1.00
## y_rep[79] 149.49 0.12 5.47 142.68 149.60 156.36 2174 1.00
## y_rep[80] 149.70 0.13 5.62 142.54 149.63 156.93 1843 1.00
## y_rep[81] 160.40 0.13 5.59 153.03 160.44 167.66 1964 1.00
## y_rep[82] 160.34 0.12 5.51 153.03 160.54 167.30 1963 1.00
## y_rep[83] 149.53 0.12 5.54 142.18 149.55 156.74 2009 1.00
## y_rep[84] 160.61 0.12 5.51 153.64 160.56 167.80 2108 1.00
## y_rep[85] 149.66 0.12 5.61 142.32 149.73 156.63 2023 1.00
## y_rep[86] 160.51 0.12 5.51 153.42 160.70 167.50 2136 1.00
## y_rep[87] 149.73 0.14 5.68 142.38 149.78 157.10 1691 1.00
## y_rep[88] 160.31 0.12 5.49 153.21 160.31 167.11 2046 1.00
## y_rep[89] 149.44 0.13 5.58 142.25 149.52 156.64 1885 1.00
## y_rep[90] 160.12 0.12 5.52 152.99 160.20 167.08 2028 1.00
## y_rep[91] 160.30 0.12 5.63 153.31 160.15 167.89 2101 1.00
## y_rep[92] 160.19 0.13 5.56 152.98 160.22 167.40 1782 1.00
## y_rep[93] 149.29 0.12 5.50 142.04 149.37 156.42 2001 1.00
## y_rep[94] 149.57 0.13 5.66 142.65 149.44 156.73 1872 1.00
## y_rep[95] 160.36 0.12 5.52 153.32 160.31 167.62 1967 1.00
## y_rep[96] 160.22 0.12 5.59 152.88 160.19 167.38 2077 1.00
## y_rep[97] 149.71 0.13 5.73 142.37 149.77 157.13 2084 1.00
## y_rep[98] 160.26 0.12 5.56 153.02 160.25 167.49 1997 1.00
## y_rep[99] 160.37 0.12 5.53 153.35 160.27 167.40 2041 1.00
## y_rep[100] 149.42 0.13 5.68 142.07 149.55 156.53 1811 1.00
## y_rep[101] 160.33 0.12 5.48 153.35 160.39 167.27 2262 1.00
## y_rep[102] 149.61 0.13 5.52 142.57 149.65 156.56 1830 1.00
## y_rep[103] 149.77 0.12 5.43 142.58 149.73 156.82 2176 1.00
## y_rep[104] 160.44 0.13 5.55 153.61 160.34 167.64 1969 1.00
## y_rep[105] 160.27 0.12 5.61 153.05 160.30 167.39 2115 1.00
## y_rep[106] 149.61 0.12 5.57 142.67 149.64 156.65 2099 1.00
## y_rep[107] 149.61 0.13 5.59 142.65 149.52 156.60 1960 1.00
## y_rep[108] 149.39 0.13 5.64 142.11 149.47 156.72 1936 1.00
## y_rep[109] 160.48 0.13 5.51 153.70 160.37 167.69 1924 1.00
## y_rep[110] 149.56 0.13 5.66 142.34 149.58 156.91 2028 1.00
## y_rep[111] 160.20 0.13 5.53 153.26 160.04 167.21 1855 1.00
## y_rep[112] 149.46 0.13 5.69 142.21 149.43 156.68 1853 1.00
## y_rep[113] 149.53 0.13 5.68 142.36 149.62 156.78 1971 1.00
## y_rep[114] 160.41 0.13 5.63 153.13 160.40 167.45 1995 1.00
## y_rep[115] 160.40 0.13 5.68 152.96 160.63 167.59 1966 1.00
## y_rep[116] 149.48 0.13 5.69 142.18 149.42 156.79 1881 1.00
## y_rep[117] 160.59 0.13 5.52 153.51 160.60 167.51 1926 1.00
## y_rep[118] 160.35 0.12 5.44 153.56 160.31 167.31 1952 1.00
## y_rep[119] 149.62 0.12 5.59 142.45 149.61 156.63 2051 1.00
## y_rep[120] 149.49 0.13 5.65 142.34 149.41 156.81 2009 1.00
## y_rep[121] 160.31 0.12 5.67 153.17 160.47 167.59 2068 1.00
## y_rep[122] 149.56 0.12 5.64 142.06 149.76 156.75 2060 1.00
## y_rep[123] 160.45 0.12 5.30 153.81 160.48 167.29 2067 1.00
## y_rep[124] 149.79 0.12 5.48 142.81 149.79 156.88 1947 1.00
## y_rep[125] 149.44 0.12 5.66 142.17 149.45 156.73 2141 1.00
## y_rep[126] 149.39 0.13 5.61 142.15 149.46 156.59 1859 1.00
## y_rep[127] 149.36 0.12 5.48 142.54 149.22 156.45 2072 1.00
## y_rep[128] 160.46 0.13 5.67 153.08 160.60 167.61 1937 1.00
## y_rep[129] 149.81 0.12 5.56 142.65 149.71 157.04 2167 1.00
## y_rep[130] 149.37 0.13 5.64 142.00 149.49 156.43 2022 1.00
## y_rep[131] 160.38 0.13 5.51 153.58 160.32 167.50 1944 1.00
## y_rep[132] 160.30 0.12 5.52 153.29 160.24 167.33 2023 1.00
## y_rep[133] 149.56 0.13 5.60 142.32 149.60 156.86 1881 1.00
## y_rep[134] 160.30 0.13 5.56 152.97 160.38 167.24 1790 1.00
## y_rep[135] 149.51 0.12 5.47 142.61 149.45 156.54 1999 1.00
## y_rep[136] 160.19 0.12 5.49 153.14 160.16 167.38 2029 1.00
## y_rep[137] 160.38 0.12 5.53 153.26 160.43 167.49 1985 1.00
## y_rep[138] 160.20 0.13 5.61 153.00 159.99 167.47 1752 1.00
## y_rep[139] 149.48 0.12 5.56 142.36 149.38 156.70 2040 1.00
## y_rep[140] 160.69 0.12 5.66 153.37 160.71 168.04 2100 1.00
## y_rep[141] 149.66 0.13 5.41 142.60 149.74 156.51 1832 1.00
## y_rep[142] 149.81 0.12 5.56 142.65 149.82 156.86 2023 1.00
## y_rep[143] 149.47 0.12 5.51 142.47 149.47 156.53 2003 1.00
## y_rep[144] 149.45 0.12 5.35 142.74 149.44 156.29 1836 1.00
## y_rep[145] 149.47 0.13 5.44 142.61 149.40 156.42 1777 1.00
## y_rep[146] 160.24 0.12 5.64 153.16 160.07 167.62 2051 1.00
## y_rep[147] 149.49 0.13 5.55 142.44 149.44 156.68 1876 1.00
## y_rep[148] 149.65 0.12 5.45 142.70 149.60 156.86 1953 1.00
## y_rep[149] 160.40 0.13 5.66 153.09 160.40 167.59 1967 1.00
## y_rep[150] 149.74 0.13 5.71 142.25 149.66 157.20 1838 1.00
## y_rep[151] 160.36 0.13 5.58 153.25 160.54 167.38 1792 1.00
## y_rep[152] 149.52 0.14 5.62 142.57 149.36 156.80 1607 1.00
## y_rep[153] 160.33 0.13 5.52 153.40 160.27 167.25 1947 1.00
## y_rep[154] 149.49 0.13 5.44 142.44 149.58 156.48 1827 1.00
## y_rep[155] 160.48 0.12 5.53 153.46 160.68 167.71 2007 1.00
## y_rep[156] 149.66 0.13 5.54 142.68 149.80 156.70 1754 1.00
## y_rep[157] 149.32 0.12 5.55 142.18 149.25 156.29 2070 1.00
## y_rep[158] 160.44 0.12 5.44 153.43 160.53 167.47 1944 1.00
## y_rep[159] 160.16 0.13 5.60 153.31 160.07 167.33 1993 1.00
## y_rep[160] 149.43 0.13 5.41 142.69 149.40 156.25 1824 1.00
## y_rep[161] 160.37 0.13 5.53 153.16 160.43 167.37 1890 1.00
## y_rep[162] 149.65 0.12 5.50 142.90 149.61 156.75 1992 1.00
## y_rep[163] 160.38 0.13 5.55 153.28 160.34 167.44 1935 1.00
## y_rep[164] 160.51 0.12 5.60 153.25 160.46 167.92 2175 1.00
## y_rep[165] 160.22 0.13 5.66 152.92 160.07 167.48 1827 1.00
## y_rep[166] 149.56 0.12 5.66 142.34 149.53 156.93 2100 1.00
## y_rep[167] 160.49 0.12 5.51 153.43 160.34 167.43 2041 1.00
## y_rep[168] 149.63 0.12 5.62 142.59 149.61 156.80 2111 1.00
## y_rep[169] 149.48 0.13 5.67 142.16 149.54 156.42 1984 1.00
## y_rep[170] 149.74 0.12 5.49 142.75 149.70 156.77 2063 1.00
## y_rep[171] 149.59 0.13 5.70 142.28 149.67 156.77 1909 1.00
## y_rep[172] 160.38 0.13 5.48 153.20 160.42 167.30 1833 1.00
## y_rep[173] 149.50 0.12 5.65 142.48 149.49 156.56 2153 1.00
## y_rep[174] 160.32 0.13 5.67 153.19 160.23 167.81 1864 1.00
## y_rep[175] 149.44 0.12 5.37 142.47 149.30 156.38 2104 1.00
## y_rep[176] 160.25 0.13 5.52 153.29 160.21 167.15 1696 1.00
## y_rep[177] 149.42 0.12 5.45 142.40 149.44 156.41 1980 1.00
## y_rep[178] 149.64 0.13 5.60 142.73 149.58 156.72 1994 1.00
## y_rep[179] 160.20 0.12 5.55 153.20 160.25 167.15 2003 1.00
## y_rep[180] 149.50 0.13 5.48 142.61 149.50 156.55 1922 1.00
## y_rep[181] 160.10 0.14 5.63 152.84 160.07 167.53 1733 1.00
## y_rep[182] 149.48 0.12 5.71 142.13 149.62 156.84 2178 1.00
## y_rep[183] 149.33 0.13 5.67 142.20 149.26 156.51 2047 1.00
## y_rep[184] 149.43 0.12 5.56 142.28 149.47 156.57 2033 1.00
## y_rep[185] 160.33 0.12 5.74 153.06 160.24 167.80 2124 1.00
## y_rep[186] 160.50 0.13 5.67 153.41 160.56 167.72 1997 1.00
## y_rep[187] 149.24 0.12 5.60 142.15 149.31 156.34 2096 1.00
## y_rep[188] 160.41 0.12 5.54 153.34 160.36 167.48 1972 1.00
## y_rep[189] 149.46 0.13 5.61 141.86 149.65 156.42 1938 1.00
## y_rep[190] 160.42 0.13 5.57 153.03 160.50 167.52 1880 1.00
## y_rep[191] 149.74 0.12 5.50 142.69 149.71 156.76 1983 1.01
## y_rep[192] 160.52 0.14 5.57 153.51 160.46 167.69 1633 1.00
## y_rep[193] 149.45 0.13 5.60 142.43 149.38 156.64 2000 1.00
## y_rep[194] 160.22 0.12 5.44 153.17 160.25 167.13 1993 1.00
## y_rep[195] 149.56 0.13 5.63 142.55 149.50 156.87 1894 1.00
## y_rep[196] 149.53 0.13 5.76 141.95 149.54 156.92 1866 1.00
## y_rep[197] 149.50 0.13 5.74 142.03 149.67 156.85 1914 1.00
## y_rep[198] 160.30 0.12 5.58 153.18 160.19 167.55 2176 1.00
## y_rep[199] 160.45 0.12 5.49 153.23 160.51 167.65 2029 1.00
## y_rep[200] 149.42 0.12 5.60 142.13 149.54 156.59 2114 1.00
## y_rep[201] 160.25 0.12 5.43 153.46 160.26 167.27 1988 1.00
## y_rep[202] 149.66 0.13 5.59 142.24 149.69 156.77 1971 1.00
## y_rep[203] 160.57 0.13 5.71 153.18 160.51 167.99 1887 1.00
## y_rep[204] 149.44 0.13 5.54 142.33 149.54 156.24 1901 1.00
## y_rep[205] 160.56 0.12 5.54 153.30 160.73 167.50 2141 1.00
## y_rep[206] 149.68 0.12 5.57 142.62 149.61 156.88 1994 1.00
## y_rep[207] 149.57 0.13 5.56 142.50 149.52 156.55 1901 1.00
## y_rep[208] 149.64 0.13 5.52 142.75 149.55 156.64 1943 1.00
## y_rep[209] 149.39 0.13 5.59 142.14 149.31 156.51 1945 1.00
## y_rep[210] 149.45 0.12 5.47 142.47 149.56 156.33 1982 1.00
## y_rep[211] 160.54 0.13 5.57 153.36 160.53 167.64 1743 1.00
## y_rep[212] 160.57 0.12 5.51 153.54 160.65 167.51 2123 1.00
## y_rep[213] 160.51 0.13 5.58 153.41 160.48 167.56 1979 1.00
## y_rep[214] 149.62 0.13 5.64 142.23 149.70 156.81 1890 1.00
## y_rep[215] 160.48 0.12 5.58 153.24 160.57 167.26 2001 1.00
## y_rep[216] 160.29 0.13 5.64 153.33 160.18 167.81 1957 1.00
## y_rep[217] 160.34 0.13 5.63 153.30 160.33 167.61 1841 1.00
## y_rep[218] 149.65 0.13 5.64 142.58 149.64 156.78 1811 1.00
## y_rep[219] 160.53 0.12 5.54 153.33 160.48 167.63 2000 1.00
## y_rep[220] 149.48 0.13 5.53 142.40 149.41 156.61 1897 1.00
## y_rep[221] 149.78 0.12 5.56 142.76 149.61 157.07 2099 1.00
## y_rep[222] 149.63 0.13 5.59 142.52 149.65 156.60 1846 1.00
## y_rep[223] 160.31 0.13 5.43 152.82 160.48 167.38 1800 1.00
## y_rep[224] 149.24 0.13 5.66 142.01 149.28 156.70 2005 1.00
## y_rep[225] 160.27 0.13 5.57 152.93 160.38 167.22 1892 1.00
## y_rep[226] 149.59 0.13 5.72 142.23 149.80 156.81 1989 1.00
## y_rep[227] 149.38 0.13 5.61 142.24 149.39 156.65 1778 1.00
## y_rep[228] 160.61 0.12 5.44 153.60 160.65 167.55 2047 1.00
## y_rep[229] 149.42 0.14 5.71 142.20 149.45 157.04 1598 1.00
## y_rep[230] 160.54 0.12 5.49 153.66 160.51 167.60 1971 1.00
## y_rep[231] 160.43 0.12 5.59 153.33 160.21 168.03 2251 1.00
## y_rep[232] 149.53 0.13 5.66 142.17 149.44 156.79 1782 1.00
## y_rep[233] 149.49 0.12 5.41 142.68 149.61 156.40 1994 1.00
## y_rep[234] 160.34 0.12 5.43 153.36 160.33 167.17 2153 1.00
## y_rep[235] 160.23 0.12 5.64 152.91 160.21 167.47 2116 1.00
## y_rep[236] 149.43 0.12 5.38 142.55 149.46 156.39 2046 1.00
## y_rep[237] 160.00 0.12 5.55 152.95 159.91 166.94 2114 1.00
## y_rep[238] 149.49 0.13 5.50 142.58 149.47 156.44 1912 1.00
## y_rep[239] 149.42 0.13 5.63 141.99 149.50 156.71 1961 1.00
## y_rep[240] 149.42 0.13 5.67 141.99 149.62 156.56 2037 1.00
## y_rep[241] 149.59 0.13 5.50 142.46 149.74 156.58 1922 1.00
## y_rep[242] 160.41 0.13 5.71 153.32 160.22 167.72 1962 1.00
## y_rep[243] 160.33 0.13 5.65 153.11 160.48 167.34 1849 1.00
## y_rep[244] 149.52 0.15 5.64 142.32 149.50 156.84 1451 1.00
## y_rep[245] 160.37 0.12 5.57 153.17 160.49 167.47 2047 1.00
## y_rep[246] 149.54 0.13 5.50 142.42 149.53 156.44 1904 1.00
## y_rep[247] 160.29 0.13 5.69 153.16 160.08 167.54 1841 1.00
## y_rep[248] 149.55 0.12 5.58 142.44 149.50 156.72 2057 1.00
## y_rep[249] 160.38 0.12 5.47 153.48 160.48 167.23 1937 1.00
## y_rep[250] 160.37 0.12 5.57 153.45 160.17 167.57 2063 1.00
## y_rep[251] 160.40 0.13 5.58 153.41 160.42 167.66 1897 1.00
## y_rep[252] 160.36 0.13 5.64 153.42 160.27 167.60 1880 1.00
## y_rep[253] 149.63 0.12 5.40 142.62 149.63 156.56 2100 1.00
## y_rep[254] 149.45 0.13 5.63 142.29 149.36 156.86 1917 1.00
## y_rep[255] 149.45 0.13 5.60 142.31 149.52 156.59 2005 1.00
## y_rep[256] 149.62 0.13 5.39 142.50 149.63 156.50 1839 1.00
## y_rep[257] 160.54 0.12 5.55 153.57 160.40 167.80 2180 1.00
## y_rep[258] 149.65 0.13 5.59 142.71 149.59 156.80 1742 1.00
## y_rep[259] 160.38 0.13 5.54 153.20 160.36 167.45 1825 1.00
## y_rep[260] 160.28 0.12 5.64 152.94 160.24 167.60 2136 1.00
## y_rep[261] 160.04 0.13 5.59 152.75 160.12 167.24 1931 1.00
## y_rep[262] 149.75 0.13 5.79 142.34 149.81 157.00 2026 1.00
## y_rep[263] 149.66 0.13 5.78 141.93 149.87 156.78 1953 1.00
## y_rep[264] 149.41 0.12 5.56 142.61 149.40 156.41 2029 1.00
## y_rep[265] 160.20 0.13 5.58 153.08 160.20 167.20 1893 1.00
## y_rep[266] 149.41 0.13 5.55 142.44 149.31 156.45 1891 1.00
## y_rep[267] 160.24 0.12 5.54 152.94 160.40 167.15 1974 1.00
## y_rep[268] 149.33 0.12 5.47 142.30 149.35 156.63 2024 1.00
## y_rep[269] 149.68 0.12 5.52 142.28 149.83 156.67 2040 1.00
## y_rep[270] 160.33 0.12 5.57 153.10 160.28 167.41 2058 1.00
## y_rep[271] 160.44 0.12 5.50 153.43 160.49 167.54 2121 1.00
## y_rep[272] 149.68 0.12 5.54 142.61 149.79 156.69 1995 1.00
## y_rep[273] 160.32 0.13 5.52 152.99 160.35 167.45 1757 1.00
## y_rep[274] 160.26 0.12 5.50 153.26 160.26 167.30 2092 1.00
## y_rep[275] 149.30 0.13 5.76 141.93 149.17 156.93 2085 1.00
## y_rep[276] 160.55 0.12 5.53 153.33 160.66 167.49 2107 1.00
## y_rep[277] 149.50 0.13 5.63 142.21 149.69 156.74 2004 1.00
## y_rep[278] 149.43 0.13 5.49 142.56 149.50 156.42 1709 1.00
## y_rep[279] 160.35 0.12 5.54 153.29 160.40 167.32 1992 1.00
## y_rep[280] 149.55 0.13 5.51 142.67 149.38 156.58 1931 1.00
## y_rep[281] 149.47 0.13 5.45 142.40 149.64 156.36 1775 1.00
## y_rep[282] 160.29 0.13 5.57 153.27 160.28 167.37 1774 1.00
## y_rep[283] 149.65 0.12 5.43 142.67 149.62 156.85 1987 1.00
## y_rep[284] 160.19 0.13 5.69 152.85 160.16 167.56 2071 1.00
## y_rep[285] 149.75 0.12 5.63 142.83 149.63 156.89 2061 1.00
## y_rep[286] 160.61 0.12 5.59 153.50 160.65 167.97 2064 1.00
## y_rep[287] 160.30 0.13 5.73 153.10 160.31 167.67 1935 1.00
## y_rep[288] 160.52 0.13 5.57 153.25 160.56 167.74 1860 1.00
## y_rep[289] 149.43 0.12 5.64 142.46 149.27 156.61 2127 1.00
## y_rep[290] 160.28 0.13 5.74 152.83 160.31 167.68 2035 1.00
## y_rep[291] 160.41 0.12 5.48 153.33 160.49 167.32 1976 1.00
## y_rep[292] 160.38 0.13 5.54 153.28 160.30 167.52 1749 1.00
## y_rep[293] 160.26 0.12 5.62 153.10 160.34 167.36 2061 1.00
## y_rep[294] 149.63 0.13 5.51 142.62 149.54 156.64 1885 1.00
## y_rep[295] 160.15 0.13 5.56 153.11 160.16 167.33 1822 1.00
## y_rep[296] 149.41 0.12 5.47 142.54 149.17 156.66 1986 1.00
## y_rep[297] 149.64 0.13 5.74 142.16 149.74 157.23 1834 1.00
## y_rep[298] 149.29 0.13 5.63 142.05 149.19 156.68 1873 1.00
## y_rep[299] 160.33 0.13 5.70 153.05 160.37 167.61 1785 1.00
## y_rep[300] 160.41 0.13 5.64 152.97 160.48 167.47 1952 1.00
## y_rep[301] 149.59 0.13 5.47 142.55 149.63 156.52 1914 1.00
## y_rep[302] 160.46 0.13 5.73 153.06 160.40 167.59 2074 1.00
## y_rep[303] 149.65 0.12 5.54 142.74 149.59 156.83 2053 1.00
## y_rep[304] 160.36 0.12 5.57 153.38 160.28 167.82 2255 1.00
## y_rep[305] 160.35 0.13 5.55 153.18 160.50 167.48 1950 1.00
## y_rep[306] 160.49 0.13 5.50 153.26 160.48 167.59 1936 1.00
## y_rep[307] 160.49 0.13 5.47 153.69 160.65 167.31 1851 1.00
## y_rep[308] 149.48 0.13 5.64 142.27 149.34 156.61 1926 1.00
## y_rep[309] 149.62 0.13 5.60 142.56 149.47 156.81 1862 1.00
## y_rep[310] 149.39 0.12 5.64 142.05 149.41 156.76 2070 1.00
## y_rep[311] 149.60 0.14 5.61 142.24 149.67 156.67 1694 1.00
## y_rep[312] 149.59 0.13 5.63 142.31 149.60 157.09 1992 1.00
## y_rep[313] 160.43 0.14 5.72 153.05 160.51 167.74 1693 1.00
## y_rep[314] 149.40 0.13 5.52 142.01 149.59 156.30 1756 1.00
## y_rep[315] 160.42 0.12 5.52 153.27 160.53 167.55 2001 1.00
## y_rep[316] 149.61 0.13 5.63 142.49 149.75 156.97 1967 1.00
## y_rep[317] 160.15 0.13 5.78 153.05 160.05 167.58 1986 1.00
## y_rep[318] 149.51 0.12 5.43 142.54 149.59 156.43 2131 1.00
## y_rep[319] 160.24 0.12 5.49 153.21 160.35 167.05 2003 1.00
## y_rep[320] 149.54 0.12 5.64 142.44 149.56 156.82 2095 1.00
## y_rep[321] 160.17 0.13 5.66 152.89 160.11 167.40 1950 1.00
## y_rep[322] 149.28 0.13 5.45 142.40 149.11 156.42 1863 1.00
## y_rep[323] 160.34 0.12 5.47 153.26 160.35 167.43 2090 1.00
## y_rep[324] 160.20 0.13 5.67 152.88 160.11 167.43 1923 1.00
## y_rep[325] 149.65 0.13 5.59 142.49 149.65 156.95 1826 1.00
## y_rep[326] 149.76 0.12 5.50 142.68 149.75 156.89 2090 1.00
## y_rep[327] 149.42 0.13 5.64 142.31 149.44 156.51 1902 1.00
## y_rep[328] 160.26 0.13 5.58 153.26 160.27 167.26 1852 1.00
## y_rep[329] 160.53 0.12 5.66 153.33 160.51 167.79 2085 1.00
## y_rep[330] 160.32 0.12 5.50 153.34 160.31 167.48 1984 1.00
## y_rep[331] 160.17 0.13 5.64 152.82 160.35 167.37 1885 1.00
## y_rep[332] 160.26 0.12 5.58 153.11 160.25 167.41 2037 1.00
## y_rep[333] 149.52 0.13 5.63 142.32 149.61 156.57 1956 1.00
## y_rep[334] 160.17 0.12 5.48 153.07 160.29 167.15 2005 1.00
## y_rep[335] 149.37 0.12 5.45 142.26 149.48 156.30 1943 1.00
## y_rep[336] 160.37 0.13 5.45 153.41 160.48 167.12 1891 1.00
## y_rep[337] 149.65 0.12 5.42 142.52 149.66 156.76 2052 1.00
## y_rep[338] 149.30 0.12 5.62 142.06 149.27 156.39 2048 1.00
## y_rep[339] 149.63 0.13 5.60 142.68 149.47 156.84 1988 1.00
## y_rep[340] 149.48 0.12 5.56 142.35 149.55 156.53 2068 1.00
## y_rep[341] 149.56 0.13 5.54 142.56 149.60 156.62 1730 1.00
## y_rep[342] 160.47 0.13 5.66 153.32 160.51 167.78 2051 1.00
## y_rep[343] 149.39 0.13 5.56 142.26 149.37 156.47 1851 1.00
## y_rep[344] 160.53 0.13 5.42 153.54 160.56 167.47 1875 1.00
## y_rep[345] 149.71 0.12 5.55 142.59 149.59 156.75 2008 1.00
## y_rep[346] 160.35 0.12 5.45 153.32 160.35 167.40 1946 1.00
## y_rep[347] 149.64 0.13 5.54 142.54 149.72 156.69 1820 1.00
## y_rep[348] 149.50 0.12 5.53 142.56 149.37 156.48 2025 1.00
## y_rep[349] 149.81 0.13 5.56 142.81 149.83 156.94 1738 1.00
## y_rep[350] 160.21 0.13 5.51 153.06 160.24 167.28 1878 1.00
## y_rep[351] 149.56 0.12 5.60 142.14 149.47 157.02 2074 1.00
## y_rep[352] 160.36 0.12 5.49 153.24 160.45 167.53 2041 1.00
## lp__ -781.30 0.04 1.18 -782.94 -781.00 -780.11 902 1.00
##
## Samples were drawn using NUTS(diag_e) at Fri Nov 22 15:25:44 2019.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).4.2 Index variable
Here we consider the variable male as an index variable, with value 1 whenever the person is a female and a value 2 whenever the person is a male.
howell2$male.index <- ifelse(howell2$male==1,2,1)
m5.2.data <- list(N = nrow(howell2), height = howell2$height, male = as.integer(howell2$male.index), n = length(unique(howell2$male.index)))
str(m5.2.data)## List of 4
## $ N : int 352
## $ height: num [1:352] 152 140 137 157 145 ...
## $ male : int [1:352] 2 1 1 2 1 2 1 2 1 2 ...
## $ n : int 2Model equation:
\[\begin{align*} h_{i} &\sim \mathcal{N}(\mu_{i} \, , \, \sigma^2) \\[4pt] \mu_{i} &= \alpha_{\text{SEX}[\textit{i}]}\\[4pt] \alpha_{j} &\sim \mathcal{N}(178,20) \quad \text{, for} \, j = 1..2\\[4pt] \sigma^2 &\sim \mathcal{U}(0,5)\\[4pt] \end{align*}\]data {
int<lower=0> N; // number of observations
int<lower=0> n; // number of levels of the categorical variable
vector[N] height; // response variables
int<lower=1,upper=n> male[N]; // categorical variable
}
parameters {
vector[n] beta; // real beta[n]; (idem) // intercepts of the categorical variable
real sigma;
}
transformed parameters {
vector[N] mu; // create one variable with predictions for each obs
for (i in 1:N) // loop for all cases
mu[i] = beta[male[i]];
}
model {
height ~ normal(mu ,sigma); // likelihood
sigma ~ cauchy(0,5);
}
generated quantities {
vector[N] y_rep;
for(i in 1:N)
y_rep[i] = normal_rng(mu[i], sigma);
}
fit.m5_2 <- sampling(m5.2, data = m5.2.data, iter = 1000, chains = 4, cores = 4)
print(fit.m5_2, probs = c(0.10, 0.5, 0.9))## Inference for Stan model: 0da8a26b283bfab1846d7d15060893cd.
## 4 chains, each with iter=1000; warmup=500; thin=1;
## post-warmup draws per chain=500, total post-warmup draws=2000.
##
## mean se_mean sd 10% 50% 90% n_eff Rhat
## beta[1] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## beta[2] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## sigma 5.54 0.01 0.22 5.27 5.53 5.82 1698 1.00
## mu[1] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[2] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[3] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[4] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[5] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[6] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[7] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[8] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[9] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[10] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[11] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[12] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[13] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[14] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[15] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[16] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[17] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[18] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[19] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[20] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[21] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[22] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[23] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[24] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[25] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[26] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[27] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[28] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[29] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[30] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[31] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[32] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[33] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[34] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[35] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[36] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[37] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[38] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[39] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[40] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[41] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[42] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[43] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[44] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[45] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[46] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[47] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[48] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[49] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[50] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[51] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[52] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[53] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[54] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[55] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[56] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[57] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[58] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[59] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[60] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[61] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[62] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[63] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[64] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[65] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[66] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[67] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[68] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[69] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[70] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[71] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[72] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[73] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[74] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[75] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[76] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[77] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[78] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[79] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[80] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[81] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[82] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[83] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[84] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[85] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[86] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[87] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[88] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[89] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[90] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[91] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[92] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[93] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[94] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[95] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[96] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[97] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[98] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[99] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[100] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[101] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[102] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[103] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[104] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[105] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[106] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[107] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[108] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[109] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[110] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[111] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[112] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[113] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[114] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[115] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[116] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[117] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[118] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[119] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[120] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[121] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[122] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[123] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[124] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[125] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[126] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[127] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[128] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[129] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[130] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[131] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[132] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[133] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[134] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[135] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[136] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[137] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[138] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[139] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[140] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[141] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[142] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[143] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[144] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[145] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[146] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[147] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[148] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[149] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[150] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[151] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[152] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[153] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[154] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[155] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[156] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[157] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[158] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[159] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[160] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[161] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[162] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[163] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[164] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[165] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[166] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[167] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[168] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[169] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[170] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[171] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[172] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[173] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[174] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[175] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[176] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[177] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[178] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[179] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[180] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[181] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[182] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[183] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[184] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[185] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[186] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[187] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[188] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[189] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[190] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[191] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[192] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[193] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[194] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[195] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[196] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[197] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[198] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[199] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[200] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[201] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[202] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[203] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[204] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[205] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[206] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[207] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[208] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[209] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[210] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[211] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[212] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[213] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[214] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[215] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[216] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[217] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[218] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[219] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[220] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[221] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[222] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[223] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[224] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[225] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[226] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[227] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[228] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[229] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[230] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[231] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[232] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[233] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[234] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[235] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[236] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[237] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[238] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[239] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[240] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[241] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[242] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[243] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[244] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[245] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[246] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[247] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[248] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[249] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[250] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[251] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[252] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[253] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[254] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[255] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[256] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[257] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[258] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[259] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[260] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[261] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[262] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[263] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[264] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[265] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[266] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[267] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[268] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[269] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[270] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[271] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[272] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[273] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[274] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[275] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[276] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[277] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[278] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[279] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[280] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[281] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[282] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[283] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[284] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[285] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[286] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[287] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[288] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[289] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[290] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[291] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[292] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[293] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[294] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[295] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[296] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[297] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[298] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[299] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[300] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[301] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[302] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[303] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[304] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[305] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[306] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[307] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[308] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[309] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[310] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[311] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[312] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[313] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[314] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[315] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[316] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[317] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[318] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[319] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[320] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[321] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[322] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[323] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[324] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[325] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[326] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[327] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[328] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[329] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[330] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[331] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[332] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[333] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[334] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[335] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[336] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[337] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[338] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[339] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[340] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[341] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[342] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[343] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[344] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[345] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[346] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[347] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[348] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[349] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[350] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## mu[351] 149.51 0.01 0.41 149.00 149.51 150.02 1769 1.00
## mu[352] 160.35 0.01 0.43 159.80 160.36 160.91 1858 1.00
## y_rep[1] 160.34 0.13 5.61 153.07 160.38 167.35 1934 1.00
## y_rep[2] 149.47 0.12 5.57 142.36 149.49 156.57 2073 1.00
## y_rep[3] 149.60 0.13 5.62 142.32 149.68 156.99 1829 1.00
## y_rep[4] 160.39 0.13 5.74 153.12 160.45 167.75 2057 1.00
## y_rep[5] 149.44 0.12 5.56 142.56 149.42 156.47 2058 1.00
## y_rep[6] 160.39 0.13 5.51 153.49 160.41 167.42 1796 1.00
## y_rep[7] 149.27 0.13 5.53 142.26 149.17 156.37 1792 1.00
## y_rep[8] 160.45 0.13 5.47 153.41 160.38 167.59 1859 1.00
## y_rep[9] 149.50 0.13 5.58 142.44 149.38 156.55 1946 1.00
## y_rep[10] 160.56 0.12 5.58 153.33 160.39 167.74 2016 1.00
## y_rep[11] 149.64 0.12 5.50 142.73 149.40 156.62 2020 1.00
## y_rep[12] 160.37 0.12 5.42 153.31 160.43 167.33 1950 1.00
## y_rep[13] 149.38 0.13 5.63 142.11 149.30 156.66 1944 1.00
## y_rep[14] 149.43 0.13 5.60 142.16 149.42 156.53 1753 1.00
## y_rep[15] 149.54 0.13 5.51 142.34 149.62 156.64 1797 1.00
## y_rep[16] 160.43 0.12 5.58 153.32 160.41 167.63 2003 1.00
## y_rep[17] 160.50 0.13 5.54 153.58 160.46 167.56 1961 1.00
## y_rep[18] 149.42 0.13 5.53 142.35 149.32 156.68 1797 1.00
## y_rep[19] 160.38 0.13 5.50 153.33 160.48 167.20 1929 1.00
## y_rep[20] 149.51 0.12 5.56 142.48 149.45 156.65 2050 1.00
## y_rep[21] 160.24 0.13 5.71 153.11 160.14 167.85 2025 1.00
## y_rep[22] 149.53 0.13 5.71 142.29 149.54 156.64 1925 1.00
## y_rep[23] 149.63 0.13 5.60 142.62 149.56 156.85 1771 1.00
## y_rep[24] 160.26 0.13 5.73 152.90 160.37 167.44 2012 1.00
## y_rep[25] 160.26 0.12 5.39 153.37 160.17 167.32 1962 1.00
## y_rep[26] 149.39 0.13 5.68 142.05 149.47 156.49 2028 1.00
## y_rep[27] 149.67 0.13 5.65 142.41 149.50 156.83 1957 1.00
## y_rep[28] 149.46 0.12 5.59 142.01 149.52 156.43 2074 1.00
## y_rep[29] 149.46 0.12 5.52 142.61 149.55 156.53 1951 1.00
## y_rep[30] 149.53 0.13 5.63 142.31 149.46 156.78 1935 1.00
## y_rep[31] 149.28 0.12 5.50 142.37 149.18 156.29 2026 1.00
## y_rep[32] 160.39 0.13 5.53 153.44 160.17 167.69 1867 1.00
## y_rep[33] 160.20 0.12 5.54 153.00 160.18 167.08 2001 1.00
## y_rep[34] 160.11 0.13 5.56 152.93 160.28 167.33 1799 1.00
## y_rep[35] 160.30 0.12 5.63 152.94 160.17 167.79 2112 1.00
## y_rep[36] 149.42 0.12 5.45 142.51 149.47 156.54 2035 1.00
## y_rep[37] 149.61 0.12 5.50 142.50 149.62 156.40 2044 1.00
## y_rep[38] 160.30 0.13 5.60 153.04 160.39 167.07 1934 1.00
## y_rep[39] 149.48 0.13 5.57 142.38 149.47 156.52 1729 1.00
## y_rep[40] 160.26 0.12 5.50 153.33 160.35 167.22 2111 1.00
## y_rep[41] 160.28 0.12 5.53 153.23 160.33 167.48 2020 1.00
## y_rep[42] 160.23 0.12 5.58 153.04 160.15 167.39 2205 1.00
## y_rep[43] 149.42 0.13 5.73 142.27 149.34 156.79 1841 1.00
## y_rep[44] 149.52 0.12 5.47 142.79 149.42 156.59 1947 1.00
## y_rep[45] 149.57 0.13 5.59 142.28 149.64 156.55 1979 1.00
## y_rep[46] 149.53 0.13 5.56 142.50 149.54 156.66 1837 1.00
## y_rep[47] 160.41 0.13 5.70 152.96 160.44 167.67 1965 1.00
## y_rep[48] 149.35 0.12 5.58 142.15 149.32 156.40 2038 1.00
## y_rep[49] 160.19 0.14 5.57 153.00 160.19 167.32 1522 1.00
## y_rep[50] 149.42 0.13 5.59 142.28 149.36 156.70 1986 1.00
## y_rep[51] 149.58 0.12 5.61 142.33 149.42 156.85 2055 1.00
## y_rep[52] 149.63 0.13 5.48 142.64 149.63 156.79 1904 1.00
## y_rep[53] 160.31 0.12 5.47 153.45 160.32 167.35 1932 1.00
## y_rep[54] 160.45 0.12 5.63 153.39 160.34 167.63 2067 1.00
## y_rep[55] 149.56 0.14 5.57 142.44 149.60 156.68 1525 1.00
## y_rep[56] 160.40 0.12 5.54 153.32 160.40 167.64 1999 1.00
## y_rep[57] 149.53 0.12 5.40 142.86 149.48 156.51 2109 1.00
## y_rep[58] 160.08 0.12 5.66 152.78 160.16 167.29 2105 1.00
## y_rep[59] 149.71 0.13 5.57 142.53 149.75 156.77 1906 1.00
## y_rep[60] 160.50 0.13 5.66 153.39 160.40 167.71 1801 1.00
## y_rep[61] 149.63 0.12 5.51 142.57 149.54 156.65 2075 1.00
## y_rep[62] 149.71 0.12 5.56 142.60 149.64 156.88 2038 1.00
## y_rep[63] 160.30 0.12 5.52 152.95 160.48 167.13 1980 1.00
## y_rep[64] 160.20 0.12 5.47 153.41 160.15 167.03 2240 1.00
## y_rep[65] 149.46 0.13 5.56 142.41 149.55 156.34 1888 1.00
## y_rep[66] 160.44 0.11 5.35 153.61 160.34 167.37 2166 1.00
## y_rep[67] 149.68 0.14 5.57 142.51 149.78 156.78 1632 1.00
## y_rep[68] 149.45 0.13 5.53 142.42 149.50 156.34 1951 1.00
## y_rep[69] 160.41 0.12 5.45 153.66 160.24 167.49 1939 1.00
## y_rep[70] 149.51 0.12 5.47 142.41 149.55 156.57 2134 1.00
## y_rep[71] 160.74 0.12 5.51 153.66 160.73 167.67 1973 1.00
## y_rep[72] 160.32 0.13 5.49 153.22 160.38 167.08 1823 1.00
## y_rep[73] 160.24 0.13 5.62 152.94 160.29 167.38 1880 1.00
## y_rep[74] 149.38 0.12 5.40 142.35 149.52 156.24 1989 1.00
## y_rep[75] 149.62 0.12 5.61 142.46 149.58 156.80 2025 1.00
## y_rep[76] 149.50 0.12 5.53 142.05 149.70 156.54 2073 1.00
## y_rep[77] 149.51 0.12 5.46 142.36 149.52 156.54 2077 1.00
## y_rep[78] 160.49 0.12 5.59 153.56 160.33 167.64 2073 1.00
## y_rep[79] 149.62 0.13 5.68 142.33 149.38 157.10 1951 1.00
## y_rep[80] 149.51 0.12 5.59 142.26 149.54 156.78 2003 1.00
## y_rep[81] 160.42 0.13 5.48 153.42 160.38 167.39 1889 1.00
## y_rep[82] 160.31 0.12 5.46 153.57 160.12 167.47 2041 1.00
## y_rep[83] 149.34 0.13 5.67 142.18 149.37 156.60 1844 1.00
## y_rep[84] 160.53 0.12 5.61 153.26 160.55 167.49 2030 1.00
## y_rep[85] 149.49 0.12 5.56 142.35 149.28 156.57 2050 1.00
## y_rep[86] 160.31 0.12 5.50 153.11 160.42 167.47 2006 1.00
## y_rep[87] 149.74 0.12 5.46 142.86 149.80 156.88 2126 1.00
## y_rep[88] 160.34 0.12 5.59 152.95 160.31 167.36 2006 1.00
## y_rep[89] 149.49 0.12 5.46 142.59 149.42 156.42 1968 1.00
## y_rep[90] 160.14 0.14 5.59 152.96 160.19 167.16 1597 1.00
## y_rep[91] 160.25 0.12 5.65 153.02 160.16 167.53 2082 1.00
## y_rep[92] 160.40 0.13 5.73 153.09 160.47 167.59 1968 1.00
## y_rep[93] 149.37 0.12 5.60 141.98 149.45 156.33 2021 1.00
## y_rep[94] 149.41 0.13 5.54 142.25 149.42 156.43 1872 1.00
## y_rep[95] 160.43 0.12 5.54 153.05 160.56 167.35 1975 1.00
## y_rep[96] 160.39 0.13 5.77 153.29 160.26 167.80 2008 1.00
## y_rep[97] 149.46 0.14 5.54 142.34 149.55 156.60 1678 1.00
## y_rep[98] 160.47 0.12 5.49 153.42 160.36 167.57 1938 1.00
## y_rep[99] 160.22 0.13 5.66 152.96 160.13 167.37 2032 1.00
## y_rep[100] 149.69 0.12 5.54 142.57 149.66 156.75 2045 1.00
## y_rep[101] 160.54 0.14 5.69 153.43 160.56 167.73 1603 1.00
## y_rep[102] 149.40 0.13 5.70 142.02 149.52 156.66 1954 1.00
## y_rep[103] 149.40 0.13 5.71 142.08 149.33 156.69 1945 1.00
## y_rep[104] 160.56 0.14 5.56 153.61 160.48 167.75 1641 1.00
## y_rep[105] 160.50 0.12 5.46 153.32 160.55 167.45 1946 1.00
## y_rep[106] 149.49 0.12 5.49 142.18 149.62 156.49 2053 1.00
## y_rep[107] 149.74 0.13 5.67 142.50 149.50 157.10 1971 1.00
## y_rep[108] 149.50 0.14 5.60 142.49 149.56 156.43 1563 1.01
## y_rep[109] 160.35 0.12 5.49 153.26 160.31 167.31 2125 1.00
## y_rep[110] 149.48 0.12 5.52 142.40 149.44 156.69 2129 1.00
## y_rep[111] 160.21 0.12 5.58 153.14 160.14 167.49 2075 1.00
## y_rep[112] 149.54 0.13 5.54 142.56 149.50 156.69 1735 1.00
## y_rep[113] 149.40 0.13 5.58 142.42 149.43 156.47 1914 1.00
## y_rep[114] 160.23 0.13 5.62 153.26 160.17 167.24 1964 1.00
## y_rep[115] 160.45 0.12 5.35 153.60 160.35 167.53 1981 1.00
## y_rep[116] 149.43 0.12 5.53 142.31 149.35 156.68 1986 1.00
## y_rep[117] 160.42 0.12 5.55 153.30 160.30 167.64 2082 1.00
## y_rep[118] 160.30 0.12 5.53 153.10 160.46 167.19 1977 1.00
## y_rep[119] 149.53 0.14 5.56 142.52 149.44 156.56 1599 1.00
## y_rep[120] 149.47 0.13 5.64 142.10 149.54 156.64 1965 1.00
## y_rep[121] 160.58 0.12 5.55 153.32 160.63 167.86 2045 1.00
## y_rep[122] 149.47 0.13 5.55 142.28 149.52 156.42 1903 1.00
## y_rep[123] 160.38 0.13 5.49 153.29 160.49 167.34 1721 1.00
## y_rep[124] 149.56 0.12 5.66 142.04 149.49 156.59 2059 1.00
## y_rep[125] 149.42 0.14 5.50 142.51 149.33 156.73 1609 1.00
## y_rep[126] 149.47 0.13 5.58 142.25 149.55 156.61 1858 1.00
## y_rep[127] 149.79 0.12 5.54 142.52 149.93 156.67 2079 1.00
## y_rep[128] 160.06 0.13 5.63 153.03 159.95 167.19 1878 1.00
## y_rep[129] 149.45 0.12 5.47 142.65 149.39 156.49 1974 1.00
## y_rep[130] 149.43 0.12 5.48 142.59 149.47 156.66 1955 1.00
## y_rep[131] 160.32 0.12 5.54 153.18 160.39 167.25 1989 1.00
## y_rep[132] 160.52 0.12 5.45 153.41 160.46 167.62 2073 1.00
## y_rep[133] 149.68 0.12 5.40 142.78 149.69 156.68 2052 1.00
## y_rep[134] 160.38 0.12 5.49 153.32 160.54 167.44 1942 1.00
## y_rep[135] 149.56 0.12 5.50 142.54 149.52 156.73 2104 1.00
## y_rep[136] 160.34 0.13 5.71 153.30 160.14 167.89 2006 1.00
## y_rep[137] 160.35 0.13 5.58 153.05 160.49 167.28 1991 1.00
## y_rep[138] 160.57 0.12 5.52 153.48 160.68 167.56 1963 1.00
## y_rep[139] 149.63 0.13 5.52 142.64 149.70 156.50 1810 1.00
## y_rep[140] 160.50 0.12 5.66 153.26 160.53 167.58 2099 1.00
## y_rep[141] 149.63 0.13 5.52 142.50 149.50 156.84 1700 1.00
## y_rep[142] 149.42 0.14 5.72 142.21 149.28 156.81 1719 1.00
## y_rep[143] 149.64 0.13 5.59 142.62 149.57 156.89 1792 1.00
## y_rep[144] 149.55 0.12 5.56 142.50 149.50 156.45 2059 1.00
## y_rep[145] 149.39 0.12 5.60 142.28 149.40 156.54 2043 1.00
## y_rep[146] 160.29 0.13 5.64 152.98 160.23 167.45 1980 1.00
## y_rep[147] 149.71 0.13 5.50 142.65 149.75 156.67 1903 1.00
## y_rep[148] 149.82 0.12 5.57 142.79 149.65 156.87 2289 1.00
## y_rep[149] 160.33 0.12 5.50 153.40 160.14 167.40 2005 1.00
## y_rep[150] 149.40 0.13 5.51 142.32 149.43 156.50 1880 1.00
## y_rep[151] 160.36 0.13 5.62 153.34 160.32 167.50 1907 1.00
## y_rep[152] 149.50 0.13 5.71 142.15 149.57 156.70 1907 1.00
## y_rep[153] 160.44 0.13 5.43 153.45 160.52 167.27 1805 1.00
## y_rep[154] 149.36 0.12 5.39 142.41 149.40 156.28 2018 1.00
## y_rep[155] 160.35 0.12 5.46 153.42 160.36 167.22 2104 1.00
## y_rep[156] 149.63 0.12 5.60 142.44 149.70 156.80 2089 1.00
## y_rep[157] 149.51 0.13 5.51 142.26 149.51 156.47 1871 1.00
## y_rep[158] 160.58 0.13 5.66 153.47 160.56 167.80 1923 1.00
## y_rep[159] 160.49 0.12 5.52 153.46 160.46 167.71 2164 1.00
## y_rep[160] 149.48 0.12 5.50 142.52 149.48 156.50 1963 1.00
## y_rep[161] 160.48 0.13 5.52 153.16 160.60 167.70 1842 1.00
## y_rep[162] 149.46 0.12 5.65 142.30 149.50 156.70 2073 1.00
## y_rep[163] 160.29 0.13 5.49 153.43 160.27 167.31 1681 1.00
## y_rep[164] 160.25 0.13 5.58 153.15 160.20 167.67 1842 1.00
## y_rep[165] 160.33 0.12 5.44 153.47 160.30 167.17 1997 1.00
## y_rep[166] 149.58 0.13 5.39 142.89 149.53 156.50 1851 1.00
## y_rep[167] 160.38 0.12 5.48 153.37 160.46 167.62 2019 1.00
## y_rep[168] 149.41 0.13 5.58 142.37 149.46 156.81 1952 1.00
## y_rep[169] 149.47 0.13 5.56 142.34 149.46 156.37 1889 1.00
## y_rep[170] 149.70 0.12 5.47 142.91 149.56 156.91 2037 1.00
## y_rep[171] 149.40 0.12 5.54 142.29 149.37 156.36 2156 1.00
## y_rep[172] 160.41 0.12 5.63 153.26 160.48 167.40 2072 1.00
## y_rep[173] 149.55 0.13 5.68 142.18 149.65 156.92 1918 1.00
## y_rep[174] 160.46 0.12 5.47 153.39 160.54 167.53 1976 1.00
## y_rep[175] 149.59 0.12 5.58 142.70 149.68 156.66 2062 1.00
## y_rep[176] 160.47 0.13 5.69 153.22 160.47 167.72 2030 1.00
## y_rep[177] 149.60 0.13 5.67 142.45 149.30 157.02 2021 1.00
## y_rep[178] 149.61 0.12 5.59 142.36 149.66 156.43 2029 1.00
## y_rep[179] 160.43 0.13 5.64 153.25 160.43 167.65 1916 1.00
## y_rep[180] 149.48 0.12 5.54 142.39 149.64 156.60 2193 1.00
## y_rep[181] 160.16 0.13 5.60 152.94 160.36 166.98 1938 1.00
## y_rep[182] 149.60 0.12 5.57 142.35 149.55 156.62 2068 1.00
## y_rep[183] 149.40 0.12 5.48 142.31 149.42 156.32 2083 1.00
## y_rep[184] 149.42 0.12 5.54 142.27 149.51 156.31 2023 1.00
## y_rep[185] 160.43 0.13 5.59 153.28 160.29 167.86 1949 1.00
## y_rep[186] 160.29 0.13 5.56 153.33 160.31 167.31 1746 1.00
## y_rep[187] 149.56 0.12 5.60 142.17 149.55 156.60 2068 1.00
## y_rep[188] 160.46 0.12 5.60 153.23 160.45 167.51 2067 1.00
## y_rep[189] 149.39 0.13 5.54 142.09 149.37 156.39 1841 1.00
## y_rep[190] 160.45 0.13 5.64 153.24 160.38 167.76 1931 1.00
## y_rep[191] 149.34 0.13 5.56 142.29 149.22 156.49 1825 1.00
## y_rep[192] 160.37 0.13 5.54 153.12 160.38 167.34 1808 1.00
## y_rep[193] 149.49 0.13 5.49 142.64 149.51 156.59 1908 1.00
## y_rep[194] 160.39 0.13 5.58 153.28 160.27 167.54 1944 1.00
## y_rep[195] 149.48 0.13 5.63 142.35 149.41 156.73 1969 1.00
## y_rep[196] 149.60 0.13 5.47 142.82 149.49 156.65 1785 1.00
## y_rep[197] 149.59 0.12 5.58 142.53 149.63 156.54 2060 1.00
## y_rep[198] 160.31 0.13 5.50 153.27 160.29 167.51 1930 1.00
## y_rep[199] 160.27 0.13 5.70 153.05 160.29 167.41 2074 1.00
## y_rep[200] 149.41 0.12 5.59 142.26 149.39 156.42 2207 1.00
## y_rep[201] 160.61 0.13 5.54 153.44 160.66 167.83 1829 1.00
## y_rep[202] 149.24 0.12 5.61 141.99 149.26 156.39 2140 1.00
## y_rep[203] 160.36 0.12 5.75 153.15 160.29 167.63 2205 1.00
## y_rep[204] 149.32 0.13 5.56 142.18 149.41 156.19 1881 1.00
## y_rep[205] 160.34 0.13 5.55 153.28 160.32 167.49 1949 1.00
## y_rep[206] 149.55 0.14 5.50 142.58 149.49 156.57 1589 1.00
## y_rep[207] 149.53 0.13 5.73 142.28 149.44 156.95 2090 1.00
## y_rep[208] 149.34 0.12 5.50 142.30 149.55 156.41 1941 1.00
## y_rep[209] 149.45 0.13 5.64 142.19 149.43 156.83 1915 1.00
## y_rep[210] 149.43 0.12 5.53 142.43 149.43 156.51 2051 1.00
## y_rep[211] 160.33 0.12 5.51 153.21 160.45 167.48 2034 1.00
## y_rep[212] 160.34 0.13 5.66 152.85 160.48 167.34 1887 1.00
## y_rep[213] 160.24 0.13 5.55 153.16 160.20 167.27 1785 1.00
## y_rep[214] 149.53 0.12 5.41 142.53 149.57 156.70 1933 1.00
## y_rep[215] 160.36 0.12 5.47 153.29 160.49 167.31 1961 1.00
## y_rep[216] 160.34 0.12 5.55 153.24 160.49 167.30 2132 1.00
## y_rep[217] 160.35 0.13 5.62 153.09 160.48 167.53 1790 1.00
## y_rep[218] 149.58 0.13 5.42 142.68 149.54 156.50 1737 1.00
## y_rep[219] 160.45 0.13 5.65 153.04 160.55 167.58 2013 1.00
## y_rep[220] 149.45 0.12 5.38 142.56 149.45 156.46 1933 1.00
## y_rep[221] 149.46 0.12 5.51 142.36 149.43 156.52 2202 1.00
## y_rep[222] 149.65 0.12 5.41 142.58 149.52 156.79 2082 1.00
## y_rep[223] 160.34 0.13 5.77 152.91 160.48 167.83 2036 1.00
## y_rep[224] 149.40 0.13 5.56 142.56 149.35 156.29 1951 1.00
## y_rep[225] 160.40 0.13 5.67 153.30 160.43 167.74 1910 1.00
## y_rep[226] 149.40 0.12 5.57 142.35 149.43 156.24 1995 1.00
## y_rep[227] 149.48 0.13 5.48 142.18 149.48 156.50 1867 1.00
## y_rep[228] 160.43 0.13 5.59 153.24 160.51 167.56 1766 1.00
## y_rep[229] 149.53 0.13 5.56 142.32 149.44 156.65 1883 1.00
## y_rep[230] 160.30 0.13 5.58 153.26 160.29 167.47 1960 1.00
## y_rep[231] 160.33 0.12 5.47 153.46 160.22 167.33 2051 1.00
## y_rep[232] 149.38 0.13 5.69 141.92 149.36 156.70 1929 1.00
## y_rep[233] 149.50 0.13 5.57 142.56 149.45 156.75 1782 1.00
## y_rep[234] 160.29 0.12 5.43 153.39 160.28 167.08 2059 1.00
## y_rep[235] 160.51 0.12 5.54 153.45 160.45 167.52 1980 1.00
## y_rep[236] 149.65 0.12 5.32 142.81 149.55 156.44 1997 1.00
## y_rep[237] 160.18 0.12 5.57 153.10 160.18 167.31 2169 1.00
## y_rep[238] 149.45 0.13 5.60 142.17 149.47 156.42 1960 1.00
## y_rep[239] 149.51 0.13 5.64 142.27 149.57 156.59 1914 1.00
## y_rep[240] 149.65 0.13 5.52 142.59 149.69 156.72 1721 1.00
## y_rep[241] 149.52 0.12 5.46 142.48 149.70 156.36 1957 1.00
## y_rep[242] 160.54 0.12 5.47 153.61 160.70 167.40 1987 1.00
## y_rep[243] 160.35 0.13 5.63 153.03 160.43 167.45 1879 1.00
## y_rep[244] 149.60 0.13 5.64 142.33 149.76 156.69 1890 1.00
## y_rep[245] 160.22 0.12 5.63 153.32 160.25 167.43 2120 1.00
## y_rep[246] 149.67 0.13 5.69 142.50 149.71 156.87 1891 1.00
## y_rep[247] 160.13 0.12 5.42 153.25 160.06 167.12 1980 1.00
## y_rep[248] 149.53 0.13 5.64 142.33 149.67 156.71 1926 1.00
## y_rep[249] 160.39 0.13 5.66 153.19 160.40 167.78 2016 1.00
## y_rep[250] 160.22 0.13 5.67 152.94 160.24 167.58 1889 1.00
## y_rep[251] 160.38 0.13 5.53 153.12 160.36 167.36 1830 1.00
## y_rep[252] 160.22 0.13 5.63 153.03 160.04 167.53 1955 1.00
## y_rep[253] 149.31 0.13 5.51 142.21 149.33 156.34 1893 1.00
## y_rep[254] 149.33 0.13 5.67 142.07 149.33 156.63 1880 1.00
## y_rep[255] 149.37 0.13 5.73 142.15 149.24 156.72 1999 1.00
## y_rep[256] 149.31 0.13 5.58 142.36 149.17 156.61 1928 1.00
## y_rep[257] 160.51 0.12 5.54 153.14 160.56 167.58 2053 1.00
## y_rep[258] 149.54 0.12 5.62 142.32 149.67 156.59 2183 1.00
## y_rep[259] 160.53 0.13 5.57 153.19 160.65 167.68 1986 1.00
## y_rep[260] 160.32 0.13 5.83 152.91 160.37 167.71 2079 1.00
## y_rep[261] 160.44 0.13 5.46 153.54 160.43 167.39 1814 1.00
## y_rep[262] 149.72 0.13 5.55 142.81 149.61 156.89 1942 1.00
## y_rep[263] 149.49 0.13 5.57 142.34 149.47 156.50 1929 1.00
## y_rep[264] 149.25 0.13 5.62 142.23 149.22 156.51 1978 1.00
## y_rep[265] 160.33 0.14 5.70 153.10 160.53 167.75 1763 1.00
## y_rep[266] 149.36 0.12 5.37 142.56 149.29 156.35 1907 1.00
## y_rep[267] 160.40 0.13 5.51 153.36 160.37 167.66 1736 1.00
## y_rep[268] 149.45 0.12 5.43 142.61 149.39 156.42 1982 1.00
## y_rep[269] 149.54 0.12 5.48 142.54 149.71 156.57 1974 1.00
## y_rep[270] 160.45 0.13 5.58 153.21 160.41 167.74 1787 1.00
## y_rep[271] 160.30 0.13 5.68 153.12 160.32 167.78 2023 1.00
## y_rep[272] 149.40 0.13 5.65 142.04 149.52 156.59 1999 1.00
## y_rep[273] 160.39 0.13 5.55 153.11 160.48 167.61 1700 1.00
## y_rep[274] 160.53 0.12 5.56 153.44 160.39 167.61 1983 1.00
## y_rep[275] 149.57 0.12 5.52 142.69 149.53 156.62 2011 1.00
## y_rep[276] 160.51 0.13 5.47 153.49 160.62 167.42 1913 1.00
## y_rep[277] 149.59 0.13 5.60 142.43 149.50 156.75 1895 1.00
## y_rep[278] 149.27 0.12 5.57 142.24 149.27 156.56 2125 1.00
## y_rep[279] 160.50 0.13 5.64 153.29 160.65 167.74 1807 1.00
## y_rep[280] 149.66 0.13 5.63 142.31 149.66 156.78 1885 1.00
## y_rep[281] 149.53 0.13 5.54 142.37 149.59 156.64 1922 1.00
## y_rep[282] 160.33 0.13 5.71 153.02 160.23 167.51 2069 1.00
## y_rep[283] 149.76 0.12 5.54 142.91 149.69 156.65 2032 1.00
## y_rep[284] 160.50 0.13 5.70 153.22 160.60 167.66 2077 1.00
## y_rep[285] 149.39 0.12 5.44 142.56 149.33 156.57 2102 1.00
## y_rep[286] 160.34 0.13 5.69 153.08 160.35 167.77 1977 1.00
## y_rep[287] 160.43 0.12 5.41 153.51 160.49 167.07 2175 1.00
## y_rep[288] 160.41 0.13 5.61 153.02 160.39 167.69 1860 1.00
## y_rep[289] 149.59 0.13 5.61 142.05 149.60 156.82 1997 1.00
## y_rep[290] 160.29 0.12 5.56 153.19 160.34 167.34 2107 1.00
## y_rep[291] 160.36 0.12 5.71 152.98 160.46 167.74 2193 1.00
## y_rep[292] 160.25 0.13 5.73 153.17 160.15 167.55 1980 1.00
## y_rep[293] 160.38 0.13 5.79 153.07 160.40 167.73 1847 1.00
## y_rep[294] 149.60 0.12 5.56 142.40 149.68 156.53 2004 1.00
## y_rep[295] 160.22 0.13 5.55 153.18 160.24 167.29 1777 1.00
## y_rep[296] 149.51 0.12 5.41 142.83 149.50 156.56 1895 1.00
## y_rep[297] 149.61 0.12 5.53 142.87 149.62 156.57 2026 1.00
## y_rep[298] 149.50 0.13 5.60 142.43 149.40 156.57 1987 1.00
## y_rep[299] 160.46 0.12 5.46 153.43 160.40 167.65 2060 1.00
## y_rep[300] 160.40 0.12 5.48 153.44 160.31 167.46 1945 1.00
## y_rep[301] 149.64 0.13 5.53 142.63 149.65 156.56 1917 1.00
## y_rep[302] 160.32 0.13 5.48 153.41 160.34 167.31 1920 1.00
## y_rep[303] 149.53 0.12 5.42 142.66 149.42 156.46 1897 1.00
## y_rep[304] 160.26 0.13 5.61 152.98 160.31 167.30 1992 1.00
## y_rep[305] 160.19 0.12 5.62 153.22 160.15 167.45 2140 1.00
## y_rep[306] 160.25 0.13 5.63 153.00 160.30 167.30 1956 1.00
## y_rep[307] 160.43 0.12 5.48 153.43 160.26 167.49 1930 1.00
## y_rep[308] 149.63 0.12 5.64 142.51 149.65 156.81 2094 1.00
## y_rep[309] 149.48 0.12 5.52 142.64 149.30 156.60 2034 1.00
## y_rep[310] 149.64 0.13 5.59 142.42 149.73 156.55 1980 1.00
## y_rep[311] 149.41 0.13 5.47 142.49 149.52 156.39 1894 1.00
## y_rep[312] 149.43 0.13 5.48 142.36 149.48 156.47 1756 1.00
## y_rep[313] 160.15 0.12 5.53 153.04 160.10 167.22 2098 1.00
## y_rep[314] 149.37 0.14 5.60 142.25 149.38 156.35 1631 1.00
## y_rep[315] 160.59 0.13 5.49 153.43 160.65 167.51 1812 1.00
## y_rep[316] 149.49 0.13 5.53 142.40 149.44 156.42 1890 1.00
## y_rep[317] 160.33 0.13 5.55 153.31 160.53 167.15 1798 1.00
## y_rep[318] 149.56 0.13 5.58 142.34 149.41 156.79 1894 1.00
## y_rep[319] 160.28 0.12 5.38 153.27 160.30 167.08 2120 1.00
## y_rep[320] 149.52 0.13 5.62 142.34 149.55 156.68 1792 1.00
## y_rep[321] 160.24 0.13 5.53 153.16 160.30 167.44 1913 1.00
## y_rep[322] 149.26 0.12 5.58 142.16 149.03 156.38 2094 1.00
## y_rep[323] 160.47 0.12 5.35 153.74 160.55 167.43 2092 1.00
## y_rep[324] 160.33 0.13 5.54 153.13 160.19 167.36 1870 1.00
## y_rep[325] 149.44 0.12 5.38 142.81 149.43 156.31 1900 1.00
## y_rep[326] 149.30 0.12 5.64 142.10 149.31 156.46 2075 1.00
## y_rep[327] 149.25 0.13 5.64 141.99 149.33 156.27 1980 1.00
## y_rep[328] 160.60 0.13 5.39 153.62 160.71 167.70 1828 1.00
## y_rep[329] 160.26 0.13 5.51 153.24 160.40 167.17 1940 1.00
## y_rep[330] 160.49 0.13 5.72 153.28 160.43 167.97 1946 1.00
## y_rep[331] 160.05 0.12 5.52 152.93 160.12 167.04 2037 1.00
## y_rep[332] 160.36 0.12 5.46 153.38 160.29 167.33 1930 1.00
## y_rep[333] 149.58 0.13 5.58 142.50 149.66 156.78 1940 1.00
## y_rep[334] 160.31 0.13 5.45 153.15 160.36 167.02 1837 1.00
## y_rep[335] 149.71 0.12 5.55 142.59 149.71 156.69 2064 1.00
## y_rep[336] 160.31 0.12 5.65 152.95 160.45 167.58 2083 1.00
## y_rep[337] 149.44 0.13 5.66 142.23 149.40 156.85 2005 1.00
## y_rep[338] 149.58 0.12 5.58 142.65 149.36 156.89 2150 1.00
## y_rep[339] 149.65 0.13 5.57 142.58 149.68 156.83 1966 1.00
## y_rep[340] 149.43 0.12 5.34 142.64 149.38 156.28 1978 1.00
## y_rep[341] 149.51 0.12 5.40 142.62 149.54 156.39 2085 1.00
## y_rep[342] 160.29 0.12 5.61 153.07 160.43 167.36 2037 1.00
## y_rep[343] 149.50 0.13 5.66 142.24 149.56 156.57 2045 1.00
## y_rep[344] 160.35 0.12 5.55 153.21 160.38 167.47 2059 1.00
## y_rep[345] 149.41 0.12 5.59 142.31 149.39 156.51 2109 1.00
## y_rep[346] 160.61 0.12 5.41 153.79 160.62 167.55 2099 1.00
## y_rep[347] 149.42 0.13 5.51 142.24 149.33 156.61 1790 1.00
## y_rep[348] 149.49 0.12 5.37 142.72 149.44 156.48 2134 1.00
## y_rep[349] 149.56 0.13 5.59 142.52 149.45 156.62 1980 1.00
## y_rep[350] 160.36 0.12 5.44 153.34 160.35 167.32 2011 1.00
## y_rep[351] 149.45 0.12 5.48 142.33 149.47 156.47 1961 1.00
## y_rep[352] 160.26 0.12 5.48 153.18 160.33 167.34 1976 1.00
## lp__ -779.77 0.04 1.27 -781.47 -779.41 -778.55 1051 1.00
##
## Samples were drawn using NUTS(diag_e) at Fri Nov 22 15:25:46 2019.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).Corresponds to a frequentist model with the intercept fixed to zero:
summary(lm(height~as.factor(male)-1,data=howell2))##
## Call:
## lm(formula = height ~ as.factor(male) - 1, data = howell2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -20.6585 -3.4635 0.2965 3.4715 18.7115
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## as.factor(male)0 149.5135 0.4049 369.2 <2e-16 ***
## as.factor(male)1 160.3585 0.4311 372.0 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.537 on 350 degrees of freedom
## Multiple R-squared: 0.9987, Adjusted R-squared: 0.9987
## F-statistic: 1.374e+05 on 2 and 350 DF, p-value: < 2.2e-16Even if you use a index variable (with values 1 or 2), you can also use the same notation as for dummy variables
X <- model.matrix(~male.index, howell2)
m5.2.bis.data <- list(N = nrow(howell2), height = howell2$height, X = X, n = length(unique(howell2$male.index)))
str(m5.2.bis.data)## List of 4
## $ N : int 352
## $ height: num [1:352] 152 140 137 157 145 ...
## $ X : num [1:352, 1:2] 1 1 1 1 1 1 1 1 1 1 ...
## ..- attr(*, "dimnames")=List of 2
## .. ..$ : chr [1:352] "1" "2" "3" "4" ...
## .. ..$ : chr [1:2] "(Intercept)" "male.index"
## ..- attr(*, "assign")= int [1:2] 0 1
## $ n : int 2data {
int<lower=0> N; // number of observations
int<lower=0> n; // number of levels of the categorical variable
vector[N] height; // response variables
matrix[N,n] X; // categorical variable
}
parameters {
vector[n] beta; // intercepts of the categorical variable
real sigma;
}
transformed parameters {
vector[N] mu;
mu = X*beta;
}
model {
height ~ normal(mu ,sigma); // likelihood
sigma ~ cauchy(0,5);
beta[1] ~ normal(178,20);
beta[2] ~ normal(0,10);
}
generated quantities {
vector[N] y_rep;
for(i in 1:N)
y_rep[i] = normal_rng(mu[i], sigma);
}
fit.m5_2_bis <- sampling(m5.2.bis, data = m5.2.bis.data, iter = 1000, chains = 4, cores = 4)
print(fit.m5_2_bis, probs = c(0.10, 0.5, 0.9))## Inference for Stan model: ea1df6c828dbad449e9a4c6c6321058c.
## 4 chains, each with iter=1000; warmup=500; thin=1;
## post-warmup draws per chain=500, total post-warmup draws=2000.
##
## mean se_mean sd 10% 50% 90% n_eff Rhat
## beta[1] 138.78 0.04 0.92 137.63 138.78 139.97 641 1.00
## beta[2] 10.77 0.02 0.59 10.00 10.76 11.53 623 1.00
## sigma 5.55 0.01 0.21 5.29 5.54 5.82 1130 1.00
## mu[1] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[2] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[3] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[4] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[5] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[6] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[7] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[8] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[9] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[10] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[11] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[12] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[13] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[14] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[15] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[16] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[17] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[18] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[19] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[20] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[21] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[22] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[23] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[24] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[25] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[26] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[27] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[28] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[29] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[30] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[31] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[32] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[33] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[34] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[35] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[36] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[37] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[38] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[39] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[40] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[41] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[42] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[43] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[44] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[45] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[46] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[47] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[48] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[49] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[50] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[51] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[52] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[53] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[54] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[55] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[56] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[57] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[58] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[59] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[60] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[61] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[62] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[63] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[64] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[65] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[66] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[67] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[68] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[69] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[70] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[71] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[72] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[73] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[74] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[75] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[76] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[77] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[78] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[79] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[80] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[81] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[82] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[83] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[84] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[85] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[86] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[87] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[88] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[89] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[90] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[91] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[92] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[93] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[94] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[95] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[96] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[97] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[98] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[99] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[100] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[101] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[102] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[103] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[104] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[105] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[106] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[107] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[108] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[109] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[110] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[111] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[112] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[113] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[114] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[115] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[116] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[117] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[118] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[119] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[120] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[121] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[122] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[123] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[124] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[125] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[126] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[127] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[128] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[129] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[130] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[131] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[132] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[133] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[134] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[135] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[136] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[137] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[138] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[139] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[140] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[141] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[142] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[143] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[144] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[145] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[146] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[147] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[148] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[149] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[150] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[151] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[152] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[153] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[154] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[155] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[156] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[157] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[158] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[159] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[160] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[161] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[162] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[163] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[164] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[165] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[166] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[167] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[168] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[169] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[170] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[171] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[172] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[173] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[174] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[175] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[176] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[177] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[178] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[179] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[180] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[181] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[182] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[183] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[184] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[185] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[186] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[187] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[188] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[189] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[190] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[191] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[192] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[193] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[194] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[195] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[196] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[197] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[198] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[199] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[200] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[201] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[202] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[203] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[204] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[205] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[206] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[207] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[208] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[209] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[210] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[211] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[212] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[213] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[214] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[215] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[216] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[217] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[218] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[219] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[220] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[221] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[222] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[223] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[224] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[225] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[226] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[227] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[228] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[229] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[230] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[231] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[232] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[233] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[234] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[235] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[236] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[237] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[238] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[239] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[240] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[241] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[242] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[243] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[244] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[245] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[246] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[247] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[248] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[249] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[250] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[251] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[252] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[253] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[254] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[255] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[256] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[257] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[258] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[259] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[260] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[261] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[262] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[263] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[264] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[265] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[266] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[267] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[268] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[269] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[270] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[271] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[272] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[273] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[274] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[275] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[276] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[277] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[278] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[279] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[280] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[281] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[282] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[283] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[284] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[285] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[286] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[287] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[288] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[289] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[290] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[291] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[292] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[293] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[294] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[295] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[296] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[297] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[298] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[299] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[300] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[301] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[302] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[303] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[304] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[305] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[306] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[307] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[308] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[309] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[310] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[311] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[312] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[313] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[314] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[315] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[316] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[317] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[318] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[319] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[320] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[321] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[322] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[323] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[324] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[325] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[326] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[327] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[328] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[329] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[330] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[331] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[332] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[333] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[334] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[335] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[336] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[337] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[338] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[339] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[340] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[341] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[342] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[343] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[344] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[345] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[346] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[347] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[348] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[349] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[350] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## mu[351] 149.55 0.01 0.40 149.04 149.54 150.05 981 1.00
## mu[352] 160.31 0.01 0.43 159.76 160.30 160.87 1246 1.00
## y_rep[1] 160.48 0.13 5.49 153.49 160.57 167.45 1821 1.00
## y_rep[2] 149.67 0.12 5.55 142.50 149.66 156.78 2059 1.00
## y_rep[3] 149.44 0.14 5.67 142.21 149.39 156.77 1749 1.00
## y_rep[4] 160.14 0.14 5.46 153.37 160.24 167.06 1540 1.00
## y_rep[5] 149.58 0.13 5.64 142.35 149.60 156.98 1889 1.00
## y_rep[6] 160.20 0.12 5.52 153.16 160.26 167.22 2145 1.00
## y_rep[7] 149.73 0.12 5.58 142.35 149.78 156.84 2133 1.00
## y_rep[8] 160.35 0.13 5.66 153.30 160.33 167.38 1834 1.00
## y_rep[9] 149.40 0.14 5.35 142.48 149.45 156.17 1443 1.00
## y_rep[10] 160.43 0.12 5.57 153.13 160.54 167.65 2145 1.00
## y_rep[11] 149.48 0.13 5.65 142.52 149.36 156.65 1837 1.00
## y_rep[12] 160.12 0.13 5.53 152.65 160.15 167.04 1841 1.00
## y_rep[13] 149.26 0.12 5.47 142.22 149.33 156.20 1964 1.00
## y_rep[14] 149.56 0.12 5.56 142.68 149.56 156.64 2001 1.00
## y_rep[15] 149.58 0.13 5.69 142.39 149.49 157.24 1797 1.00
## y_rep[16] 160.33 0.13 5.74 153.00 160.37 167.62 2001 1.00
## y_rep[17] 160.45 0.13 5.51 153.34 160.31 167.63 1938 1.00
## y_rep[18] 149.58 0.14 5.61 142.54 149.59 156.54 1704 1.00
## y_rep[19] 160.34 0.13 5.57 153.16 160.19 167.74 1963 1.00
## y_rep[20] 149.63 0.12 5.57 142.72 149.58 156.59 2162 1.00
## y_rep[21] 160.54 0.13 5.65 153.21 160.41 167.89 1998 1.00
## y_rep[22] 149.59 0.13 5.66 142.20 149.57 156.88 1811 1.00
## y_rep[23] 149.58 0.13 5.52 142.56 149.54 156.79 1876 1.00
## y_rep[24] 160.28 0.12 5.39 153.42 160.26 167.17 1865 1.00
## y_rep[25] 160.30 0.13 5.57 153.08 160.28 167.20 1962 1.00
## y_rep[26] 149.81 0.13 5.68 142.56 149.76 157.09 1802 1.00
## y_rep[27] 149.76 0.13 5.70 142.57 149.81 156.86 1967 1.00
## y_rep[28] 149.64 0.12 5.61 142.23 149.81 156.60 2145 1.00
## y_rep[29] 149.35 0.12 5.57 142.15 149.32 156.47 2015 1.00
## y_rep[30] 149.64 0.13 5.66 142.35 149.75 156.84 2026 1.00
## y_rep[31] 149.61 0.13 5.58 142.24 149.72 156.77 1879 1.00
## y_rep[32] 160.42 0.13 5.74 153.03 160.40 167.63 1957 1.00
## y_rep[33] 160.26 0.13 5.60 153.06 160.25 167.28 1913 1.00
## y_rep[34] 160.28 0.13 5.57 153.10 160.29 167.17 1905 1.00
## y_rep[35] 160.34 0.12 5.49 153.44 160.16 167.34 2009 1.00
## y_rep[36] 149.44 0.13 5.52 142.27 149.45 156.51 1697 1.00
## y_rep[37] 149.57 0.13 5.46 142.33 149.47 156.59 1802 1.00
## y_rep[38] 160.43 0.13 5.69 153.26 160.33 167.76 1785 1.00
## y_rep[39] 149.60 0.12 5.55 142.22 149.58 156.80 1993 1.00
## y_rep[40] 160.17 0.13 5.54 153.07 160.29 167.38 1955 1.00
## y_rep[41] 160.21 0.12 5.59 153.02 160.31 167.34 2071 1.00
## y_rep[42] 160.29 0.13 5.61 153.18 160.18 167.59 1980 1.00
## y_rep[43] 149.56 0.13 5.60 142.35 149.63 156.61 1845 1.00
## y_rep[44] 149.57 0.13 5.56 142.35 149.57 156.45 1920 1.00
## y_rep[45] 149.42 0.13 5.73 141.89 149.55 156.50 1901 1.00
## y_rep[46] 149.75 0.12 5.57 142.64 149.72 157.08 1999 1.00
## y_rep[47] 160.29 0.13 5.74 153.08 160.28 167.54 1847 1.00
## y_rep[48] 149.41 0.12 5.45 142.47 149.28 156.55 2005 1.00
## y_rep[49] 160.38 0.12 5.48 153.32 160.48 167.26 1958 1.00
## y_rep[50] 149.79 0.13 5.58 142.86 149.73 156.95 1717 1.00
## y_rep[51] 149.42 0.14 5.46 142.52 149.60 156.28 1605 1.00
## y_rep[52] 149.69 0.13 5.58 142.36 149.77 156.65 1904 1.00
## y_rep[53] 160.33 0.13 5.52 153.07 160.36 167.39 1678 1.00
## y_rep[54] 160.42 0.12 5.49 153.27 160.26 167.38 2138 1.00
## y_rep[55] 149.49 0.13 5.69 142.20 149.41 156.61 1853 1.00
## y_rep[56] 160.12 0.13 5.46 153.26 160.03 167.29 1860 1.00
## y_rep[57] 149.41 0.12 5.60 142.35 149.41 156.90 2099 1.00
## y_rep[58] 160.22 0.13 5.58 153.07 160.21 167.38 1921 1.00
## y_rep[59] 149.21 0.13 5.69 141.82 149.32 156.45 1999 1.00
## y_rep[60] 160.04 0.14 5.71 152.77 160.13 167.49 1777 1.00
## y_rep[61] 149.59 0.13 5.58 142.33 149.57 156.83 1920 1.00
## y_rep[62] 149.43 0.13 5.66 142.30 149.39 156.76 1928 1.00
## y_rep[63] 160.09 0.14 5.76 152.80 159.94 167.59 1727 1.00
## y_rep[64] 160.30 0.13 5.67 152.97 160.40 167.38 2010 1.00
## y_rep[65] 149.59 0.12 5.55 142.47 149.55 156.78 2006 1.00
## y_rep[66] 160.05 0.12 5.37 153.11 160.04 166.97 2033 1.00
## y_rep[67] 149.45 0.12 5.54 142.45 149.45 156.57 1963 1.00
## y_rep[68] 149.47 0.14 5.45 142.52 149.69 156.44 1557 1.00
## y_rep[69] 160.51 0.12 5.64 153.10 160.66 167.79 2051 1.00
## y_rep[70] 149.50 0.12 5.62 142.18 149.46 156.82 2083 1.00
## y_rep[71] 160.32 0.12 5.51 153.17 160.44 167.28 1982 1.00
## y_rep[72] 160.02 0.13 5.76 152.40 160.00 167.45 1920 1.00
## y_rep[73] 160.18 0.12 5.62 152.83 160.14 167.33 2121 1.00
## y_rep[74] 149.56 0.13 5.68 142.16 149.61 156.71 1853 1.00
## y_rep[75] 149.54 0.12 5.48 142.46 149.47 156.57 2085 1.00
## y_rep[76] 149.51 0.14 5.58 142.24 149.45 156.70 1688 1.00
## y_rep[77] 149.58 0.12 5.62 142.53 149.49 156.83 2121 1.00
## y_rep[78] 160.21 0.13 5.58 152.98 160.17 167.52 1952 1.00
## y_rep[79] 149.73 0.13 5.69 142.68 149.71 156.86 1925 1.00
## y_rep[80] 149.44 0.13 5.61 142.48 149.37 156.58 1950 1.00
## y_rep[81] 160.06 0.13 5.68 152.87 159.94 167.24 1920 1.00
## y_rep[82] 160.21 0.12 5.52 153.20 160.18 167.29 2130 1.00
## y_rep[83] 149.54 0.12 5.49 142.27 149.54 156.37 1977 1.00
## y_rep[84] 160.46 0.12 5.64 153.43 160.41 167.66 2132 1.00
## y_rep[85] 149.32 0.12 5.47 142.39 149.34 156.26 2014 1.00
## y_rep[86] 160.23 0.12 5.54 153.21 160.12 167.35 2071 1.00
## y_rep[87] 149.55 0.14 5.51 142.62 149.73 156.51 1621 1.00
## y_rep[88] 160.59 0.12 5.50 153.53 160.56 167.64 1977 1.00
## y_rep[89] 149.57 0.12 5.52 142.63 149.53 156.71 2114 1.00
## y_rep[90] 160.30 0.13 5.79 152.75 160.24 167.55 2111 1.00
## y_rep[91] 160.19 0.12 5.39 153.34 159.93 167.07 1997 1.00
## y_rep[92] 160.26 0.13 5.62 153.08 160.38 167.26 1972 1.00
## y_rep[93] 149.59 0.13 5.40 142.67 149.69 156.59 1614 1.00
## y_rep[94] 149.49 0.13 5.52 142.49 149.62 156.33 1922 1.00
## y_rep[95] 160.39 0.12 5.50 153.29 160.34 167.43 1967 1.00
## y_rep[96] 160.49 0.13 5.48 153.13 160.49 167.59 1865 1.00
## y_rep[97] 149.54 0.13 5.65 142.18 149.70 156.56 2041 1.00
## y_rep[98] 160.19 0.12 5.58 152.96 160.28 167.33 2128 1.00
## y_rep[99] 160.48 0.14 5.63 153.31 160.45 167.91 1737 1.00
## y_rep[100] 149.42 0.13 5.45 142.31 149.57 156.28 1671 1.00
## y_rep[101] 160.40 0.13 5.62 153.34 160.52 167.40 1988 1.00
## y_rep[102] 149.52 0.13 5.58 142.30 149.71 156.39 1987 1.00
## y_rep[103] 149.39 0.12 5.58 142.19 149.56 156.52 2032 1.00
## y_rep[104] 160.27 0.12 5.60 153.23 160.17 167.54 2080 1.00
## y_rep[105] 160.33 0.13 5.61 153.32 160.19 167.50 2005 1.00
## y_rep[106] 149.56 0.13 5.62 142.36 149.71 156.64 1982 1.00
## y_rep[107] 149.53 0.12 5.54 142.52 149.58 156.82 2150 1.00
## y_rep[108] 149.61 0.12 5.48 142.58 149.58 156.81 2051 1.00
## y_rep[109] 160.10 0.12 5.63 153.01 160.05 167.27 2100 1.00
## y_rep[110] 149.62 0.12 5.51 142.48 149.61 156.60 1992 1.00
## y_rep[111] 160.28 0.13 5.61 153.19 160.39 167.34 1897 1.00
## y_rep[112] 149.58 0.12 5.49 142.42 149.70 156.53 2047 1.00
## y_rep[113] 149.53 0.13 5.58 142.28 149.60 156.63 1911 1.00
## y_rep[114] 160.10 0.13 5.45 153.23 160.06 166.99 1812 1.00
## y_rep[115] 160.23 0.13 5.60 153.06 160.26 167.48 1820 1.00
## y_rep[116] 149.66 0.13 5.56 142.46 149.82 156.65 1887 1.00
## y_rep[117] 160.35 0.13 5.60 153.12 160.37 167.61 1855 1.00
## y_rep[118] 160.19 0.13 5.70 152.94 160.27 167.36 1964 1.00
## y_rep[119] 149.47 0.12 5.58 142.32 149.33 156.63 2037 1.00
## y_rep[120] 149.74 0.13 5.64 142.39 149.71 156.89 1959 1.00
## y_rep[121] 160.29 0.13 5.52 153.22 160.30 167.39 1901 1.00
## y_rep[122] 149.59 0.13 5.60 142.30 149.61 156.82 1949 1.00
## y_rep[123] 160.24 0.12 5.59 153.10 160.28 167.09 2013 1.00
## y_rep[124] 149.52 0.13 5.59 142.68 149.32 156.72 1965 1.00
## y_rep[125] 149.52 0.12 5.51 142.52 149.46 156.56 2035 1.00
## y_rep[126] 149.58 0.13 5.62 142.40 149.50 156.79 1998 1.00
## y_rep[127] 149.59 0.12 5.56 142.68 149.53 156.49 2256 1.00
## y_rep[128] 160.41 0.13 5.62 153.22 160.42 167.59 1781 1.00
## y_rep[129] 149.38 0.12 5.46 142.15 149.50 156.35 1944 1.00
## y_rep[130] 149.52 0.13 5.57 142.38 149.40 156.67 1916 1.00
## y_rep[131] 160.23 0.13 5.73 152.94 160.11 167.61 1844 1.00
## y_rep[132] 160.24 0.12 5.55 152.99 160.41 167.07 2001 1.00
## y_rep[133] 149.63 0.12 5.50 142.81 149.66 156.48 1952 1.00
## y_rep[134] 160.44 0.12 5.63 153.16 160.44 167.46 2033 1.00
## y_rep[135] 149.52 0.13 5.55 142.27 149.55 156.46 1897 1.00
## y_rep[136] 160.06 0.13 5.70 152.72 159.92 167.58 1878 1.00
## y_rep[137] 160.36 0.13 5.67 153.15 160.53 167.42 1889 1.00
## y_rep[138] 160.45 0.12 5.50 153.46 160.36 167.63 2001 1.00
## y_rep[139] 149.66 0.13 5.68 142.13 149.62 156.97 1897 1.00
## y_rep[140] 160.26 0.12 5.53 153.29 160.20 167.36 2125 1.00
## y_rep[141] 149.59 0.12 5.67 142.49 149.62 156.78 2109 1.00
## y_rep[142] 149.41 0.12 5.48 142.30 149.52 156.35 2029 1.00
## y_rep[143] 149.46 0.12 5.54 142.74 149.41 156.44 1982 1.00
## y_rep[144] 149.57 0.13 5.57 142.29 149.70 156.65 1896 1.00
## y_rep[145] 149.55 0.12 5.58 142.33 149.65 156.42 2038 1.00
## y_rep[146] 160.39 0.13 5.41 153.44 160.32 167.30 1826 1.00
## y_rep[147] 149.44 0.13 5.67 142.30 149.29 156.74 2012 1.00
## y_rep[148] 149.61 0.13 5.67 142.20 149.60 156.89 2002 1.00
## y_rep[149] 160.46 0.12 5.63 153.47 160.38 167.56 2208 1.00
## y_rep[150] 149.42 0.13 5.60 142.03 149.44 156.57 1934 1.00
## y_rep[151] 160.07 0.13 5.59 153.10 159.95 167.04 1949 1.00
## y_rep[152] 149.71 0.13 5.56 142.52 149.75 156.92 1898 1.00
## y_rep[153] 160.28 0.13 5.48 153.23 160.30 167.26 1650 1.00
## y_rep[154] 149.57 0.13 5.54 142.37 149.58 156.70 1743 1.00
## y_rep[155] 160.48 0.12 5.50 153.69 160.49 167.57 2112 1.00
## y_rep[156] 149.60 0.13 5.52 142.44 149.68 156.71 1800 1.00
## y_rep[157] 149.63 0.13 5.53 142.57 149.55 156.60 1936 1.00
## y_rep[158] 160.49 0.13 5.50 153.60 160.45 167.46 1804 1.00
## y_rep[159] 160.38 0.13 5.52 153.28 160.30 167.52 1800 1.00
## y_rep[160] 149.62 0.12 5.50 142.57 149.65 156.75 2115 1.00
## y_rep[161] 160.50 0.12 5.52 153.26 160.46 167.59 1973 1.00
## y_rep[162] 149.31 0.13 5.72 141.74 149.38 156.60 1930 1.00
## y_rep[163] 160.29 0.13 5.72 152.86 160.44 167.50 1983 1.00
## y_rep[164] 160.10 0.13 5.74 152.82 159.99 167.35 1948 1.00
## y_rep[165] 160.29 0.13 5.54 153.13 160.41 167.21 1965 1.00
## y_rep[166] 149.75 0.13 5.62 142.38 149.73 156.98 1995 1.00
## y_rep[167] 160.23 0.13 5.55 153.38 160.23 167.51 1965 1.00
## y_rep[168] 149.58 0.12 5.59 142.29 149.61 156.79 2110 1.00
## y_rep[169] 149.46 0.13 5.52 142.66 149.44 156.51 1936 1.00
## y_rep[170] 149.39 0.14 5.59 142.23 149.38 156.66 1665 1.00
## y_rep[171] 149.39 0.13 5.61 142.19 149.44 156.51 1820 1.00
## y_rep[172] 160.35 0.12 5.50 153.45 160.37 167.50 2023 1.00
## y_rep[173] 149.72 0.13 5.58 142.41 149.89 156.59 1872 1.00
## y_rep[174] 160.39 0.12 5.55 153.24 160.44 167.28 1971 1.00
## y_rep[175] 149.50 0.13 5.73 142.22 149.52 156.95 1940 1.00
## y_rep[176] 160.22 0.12 5.60 152.97 160.39 167.40 2059 1.00
## y_rep[177] 149.41 0.13 5.55 142.45 149.18 156.69 1914 1.00
## y_rep[178] 149.61 0.13 5.67 142.21 149.63 156.81 1968 1.00
## y_rep[179] 160.49 0.13 5.79 152.97 160.54 168.03 2056 1.00
## y_rep[180] 149.49 0.12 5.45 142.53 149.44 156.34 2060 1.00
## y_rep[181] 160.20 0.13 5.51 153.11 160.03 167.09 1877 1.00
## y_rep[182] 149.35 0.12 5.73 142.04 149.31 156.72 2138 1.00
## y_rep[183] 149.35 0.13 5.43 142.39 149.33 156.05 1844 1.00
## y_rep[184] 149.48 0.13 5.67 142.10 149.65 156.83 1998 1.00
## y_rep[185] 160.38 0.12 5.48 153.26 160.30 167.48 2064 1.00
## y_rep[186] 160.37 0.12 5.55 153.19 160.32 167.57 1975 1.00
## y_rep[187] 149.65 0.13 5.57 142.66 149.61 156.88 1721 1.00
## y_rep[188] 160.41 0.12 5.46 153.52 160.34 167.46 1985 1.00
## y_rep[189] 149.75 0.13 5.67 142.46 149.80 157.00 1918 1.00
## y_rep[190] 160.14 0.13 5.55 152.94 160.15 167.13 1939 1.00
## y_rep[191] 149.65 0.13 5.52 142.54 149.65 156.76 1869 1.00
## y_rep[192] 160.35 0.13 5.60 153.06 160.28 167.44 1946 1.00
## y_rep[193] 149.46 0.12 5.48 142.31 149.53 156.34 2012 1.00
## y_rep[194] 160.13 0.13 5.53 152.95 160.09 167.32 1954 1.00
## y_rep[195] 149.56 0.13 5.61 142.45 149.47 156.98 1968 1.00
## y_rep[196] 149.19 0.13 5.60 142.23 149.28 156.51 1785 1.00
## y_rep[197] 149.59 0.14 5.56 142.44 149.70 156.59 1567 1.00
## y_rep[198] 160.43 0.12 5.50 153.37 160.34 167.75 2052 1.00
## y_rep[199] 160.27 0.12 5.55 153.20 160.25 167.44 1981 1.00
## y_rep[200] 149.37 0.13 5.60 142.31 149.22 156.57 1935 1.00
## y_rep[201] 160.39 0.13 5.65 153.27 160.34 167.42 1820 1.00
## y_rep[202] 149.63 0.13 5.60 142.45 149.67 156.51 1908 1.00
## y_rep[203] 160.29 0.13 5.54 153.13 160.25 167.57 1895 1.00
## y_rep[204] 149.57 0.13 5.71 142.34 149.55 156.89 1873 1.00
## y_rep[205] 160.31 0.13 5.76 152.99 160.24 167.88 1917 1.00
## y_rep[206] 149.62 0.12 5.53 142.71 149.55 156.62 2050 1.00
## y_rep[207] 149.43 0.13 5.42 142.61 149.38 156.53 1829 1.00
## y_rep[208] 149.40 0.13 5.61 142.27 149.43 156.68 1951 1.00
## y_rep[209] 149.58 0.12 5.55 142.33 149.70 156.58 2002 1.00
## y_rep[210] 149.50 0.12 5.56 142.42 149.42 156.77 2075 1.00
## y_rep[211] 160.42 0.12 5.59 153.48 160.36 167.37 2049 1.00
## y_rep[212] 160.20 0.12 5.44 152.99 160.33 166.99 1931 1.00
## y_rep[213] 160.15 0.13 5.51 153.44 159.88 167.00 1755 1.00
## y_rep[214] 149.62 0.13 5.63 142.05 149.84 156.66 1795 1.00
## y_rep[215] 160.35 0.12 5.52 153.26 160.39 167.26 2116 1.00
## y_rep[216] 160.51 0.13 5.54 153.34 160.54 167.60 1831 1.00
## y_rep[217] 160.11 0.12 5.45 153.14 160.14 167.03 2136 1.00
## y_rep[218] 149.69 0.12 5.51 142.65 149.70 156.74 2137 1.00
## y_rep[219] 160.04 0.14 5.57 152.87 160.08 167.16 1621 1.00
## y_rep[220] 149.60 0.13 5.62 142.42 149.63 156.79 1991 1.00
## y_rep[221] 149.61 0.12 5.40 142.75 149.55 156.57 1954 1.00
## y_rep[222] 149.60 0.12 5.54 142.60 149.56 156.74 2039 1.00
## y_rep[223] 160.35 0.12 5.47 153.47 160.40 167.12 1955 1.00
## y_rep[224] 149.66 0.12 5.62 142.59 149.69 156.81 2046 1.00
## y_rep[225] 160.51 0.12 5.53 153.66 160.35 167.62 2051 1.00
## y_rep[226] 149.55 0.11 5.48 142.59 149.51 156.53 2401 1.00
## y_rep[227] 149.29 0.12 5.62 142.39 149.18 156.39 2062 1.00
## y_rep[228] 160.36 0.13 5.53 153.47 160.37 167.28 1756 1.00
## y_rep[229] 149.50 0.13 5.60 142.30 149.53 156.61 1943 1.00
## y_rep[230] 160.29 0.13 5.58 153.11 160.32 167.61 1874 1.00
## y_rep[231] 160.22 0.13 5.64 153.27 160.21 167.57 1759 1.00
## y_rep[232] 149.57 0.13 5.65 142.34 149.42 156.81 1794 1.00
## y_rep[233] 149.29 0.13 5.57 141.96 149.44 156.45 1970 1.00
## y_rep[234] 160.21 0.13 5.60 153.08 160.13 167.38 1983 1.00
## y_rep[235] 160.07 0.13 5.52 153.05 160.13 167.02 1936 1.00
## y_rep[236] 149.75 0.13 5.44 142.49 149.66 156.82 1883 1.00
## y_rep[237] 160.37 0.12 5.41 153.44 160.29 167.34 2059 1.00
## y_rep[238] 149.59 0.13 5.53 142.67 149.65 156.68 1797 1.00
## y_rep[239] 149.53 0.12 5.59 142.44 149.50 156.95 2083 1.00
## y_rep[240] 149.38 0.12 5.50 142.46 149.38 156.44 1986 1.00
## y_rep[241] 149.52 0.12 5.55 142.48 149.46 156.57 1996 1.00
## y_rep[242] 160.39 0.12 5.63 153.00 160.47 167.44 2086 1.00
## y_rep[243] 160.65 0.13 5.47 153.74 160.72 167.81 1825 1.00
## y_rep[244] 149.48 0.13 5.66 142.36 149.39 156.82 1981 1.00
## y_rep[245] 160.29 0.12 5.71 152.83 160.31 167.54 2226 1.00
## y_rep[246] 149.50 0.13 5.73 142.28 149.62 156.87 1889 1.00
## y_rep[247] 160.20 0.12 5.56 153.27 160.15 167.09 2023 1.00
## y_rep[248] 149.67 0.13 5.62 142.20 149.71 156.85 1819 1.00
## y_rep[249] 160.29 0.13 5.48 153.24 160.22 167.35 1874 1.00
## y_rep[250] 160.33 0.13 5.69 152.98 160.38 167.76 2013 1.00
## y_rep[251] 160.25 0.12 5.51 153.25 160.30 167.45 2074 1.00
## y_rep[252] 160.25 0.12 5.58 153.15 160.27 167.10 2182 1.00
## y_rep[253] 149.35 0.13 5.68 141.96 149.33 156.64 1981 1.00
## y_rep[254] 149.65 0.13 5.47 142.70 149.76 156.52 1899 1.00
## y_rep[255] 149.63 0.12 5.53 142.70 149.52 156.75 2022 1.00
## y_rep[256] 149.53 0.13 5.66 142.19 149.52 156.91 1918 1.00
## y_rep[257] 160.41 0.13 5.52 153.23 160.47 167.37 1948 1.00
## y_rep[258] 149.40 0.12 5.57 142.36 149.33 156.57 2018 1.00
## y_rep[259] 160.06 0.13 5.69 152.91 160.06 167.14 1948 1.00
## y_rep[260] 160.35 0.12 5.49 153.37 160.31 167.56 1954 1.00
## y_rep[261] 160.34 0.12 5.55 153.05 160.33 167.48 2162 1.00
## y_rep[262] 149.60 0.12 5.36 142.83 149.58 156.37 1940 1.00
## y_rep[263] 149.55 0.13 5.55 142.73 149.56 156.52 1889 1.00
## y_rep[264] 149.63 0.13 5.55 142.75 149.54 156.95 1846 1.00
## y_rep[265] 160.35 0.13 5.50 153.40 160.43 167.26 1811 1.00
## y_rep[266] 149.38 0.13 5.57 142.42 149.17 156.47 1826 1.00
## y_rep[267] 160.28 0.13 5.64 153.18 160.29 167.61 1846 1.00
## y_rep[268] 149.60 0.14 5.65 142.64 149.52 156.72 1557 1.00
## y_rep[269] 149.53 0.13 5.62 142.43 149.45 156.73 1847 1.00
## y_rep[270] 160.41 0.13 5.47 153.51 160.49 167.31 1675 1.00
## y_rep[271] 160.33 0.13 5.64 153.12 160.38 167.42 1995 1.00
## y_rep[272] 149.44 0.12 5.51 142.40 149.52 156.47 2178 1.00
## y_rep[273] 160.28 0.14 5.58 153.23 160.12 167.56 1645 1.00
## y_rep[274] 160.55 0.13 5.43 153.53 160.59 167.46 1861 1.00
## y_rep[275] 149.30 0.13 5.60 142.16 149.33 156.36 1988 1.00
## y_rep[276] 160.41 0.12 5.51 153.23 160.47 167.52 2025 1.00
## y_rep[277] 149.64 0.12 5.61 142.33 149.73 156.92 2075 1.00
## y_rep[278] 149.43 0.13 5.50 142.43 149.37 156.39 1714 1.00
## y_rep[279] 160.43 0.13 5.65 153.24 160.54 167.59 1944 1.00
## y_rep[280] 149.60 0.14 5.61 142.49 149.64 156.72 1673 1.00
## y_rep[281] 149.72 0.13 5.61 142.53 149.64 156.74 1921 1.00
## y_rep[282] 160.06 0.12 5.59 152.93 160.15 167.36 2134 1.00
## y_rep[283] 149.42 0.13 5.62 142.20 149.47 156.68 1990 1.00
## y_rep[284] 160.18 0.13 5.61 153.15 160.09 167.31 1994 1.00
## y_rep[285] 149.73 0.12 5.56 142.68 149.59 157.12 2012 1.00
## y_rep[286] 160.28 0.13 5.69 153.19 160.14 167.65 1983 1.00
## y_rep[287] 160.22 0.12 5.42 153.53 160.06 167.18 1952 1.00
## y_rep[288] 160.31 0.13 5.57 153.18 160.32 167.50 1774 1.00
## y_rep[289] 149.63 0.13 5.59 142.49 149.60 156.93 1876 1.00
## y_rep[290] 160.39 0.13 5.52 153.19 160.38 167.27 1749 1.00
## y_rep[291] 160.13 0.12 5.53 153.06 160.02 167.23 2082 1.00
## y_rep[292] 160.28 0.13 5.50 153.32 160.48 167.14 1932 1.00
## y_rep[293] 160.27 0.14 5.65 152.86 160.55 167.25 1529 1.00
## y_rep[294] 149.43 0.13 5.56 142.08 149.40 156.36 1959 1.00
## y_rep[295] 160.33 0.13 5.61 153.15 160.51 167.68 2006 1.00
## y_rep[296] 149.55 0.13 5.65 142.05 149.59 156.71 1958 1.00
## y_rep[297] 149.77 0.13 5.47 142.64 149.88 156.54 1659 1.00
## y_rep[298] 149.48 0.13 5.40 142.63 149.46 156.17 1844 1.00
## y_rep[299] 160.36 0.13 5.74 153.23 160.38 167.89 2009 1.00
## y_rep[300] 160.42 0.13 5.50 153.31 160.53 167.40 1786 1.00
## y_rep[301] 149.54 0.13 5.59 142.63 149.52 156.66 1889 1.00
## y_rep[302] 160.12 0.12 5.65 153.11 160.00 167.38 2093 1.00
## y_rep[303] 149.53 0.13 5.51 142.62 149.45 156.43 1887 1.00
## y_rep[304] 160.32 0.13 5.70 153.00 160.36 167.71 1790 1.00
## y_rep[305] 160.52 0.12 5.44 153.36 160.69 167.62 1935 1.00
## y_rep[306] 160.29 0.13 5.77 152.70 160.32 168.06 1996 1.00
## y_rep[307] 160.51 0.13 5.61 153.32 160.52 167.51 1899 1.00
## y_rep[308] 149.87 0.12 5.55 142.89 149.79 157.07 2048 1.00
## y_rep[309] 149.69 0.14 5.74 142.32 149.65 157.07 1712 1.00
## y_rep[310] 149.64 0.13 5.54 142.38 149.62 156.99 1843 1.00
## y_rep[311] 149.49 0.12 5.60 142.42 149.41 156.65 2115 1.00
## y_rep[312] 149.49 0.13 5.61 142.45 149.50 156.72 1823 1.00
## y_rep[313] 160.33 0.12 5.45 153.44 160.22 167.49 1983 1.00
## y_rep[314] 149.20 0.13 5.62 142.10 148.91 156.38 1977 1.00
## y_rep[315] 160.51 0.13 5.62 153.28 160.53 167.81 1848 1.00
## y_rep[316] 149.55 0.14 5.64 142.29 149.44 156.87 1591 1.00
## y_rep[317] 160.15 0.12 5.70 152.74 160.34 167.23 2116 1.00
## y_rep[318] 149.50 0.13 5.62 141.98 149.44 156.54 1835 1.00
## y_rep[319] 160.22 0.13 5.46 152.96 160.29 167.18 1797 1.00
## y_rep[320] 149.58 0.13 5.66 142.42 149.47 157.05 1986 1.00
## y_rep[321] 160.46 0.13 5.70 153.24 160.58 167.83 1884 1.00
## y_rep[322] 149.60 0.12 5.58 142.52 149.69 156.70 2077 1.00
## y_rep[323] 160.38 0.12 5.59 153.16 160.34 167.58 1999 1.00
## y_rep[324] 160.20 0.12 5.56 153.19 160.14 167.30 2045 1.00
## y_rep[325] 149.70 0.12 5.48 142.61 149.67 156.82 1928 1.00
## y_rep[326] 149.49 0.12 5.67 142.30 149.48 156.72 2093 1.00
## y_rep[327] 149.57 0.12 5.52 142.38 149.66 156.84 2062 1.00
## y_rep[328] 160.43 0.14 5.52 153.50 160.40 167.54 1547 1.00
## y_rep[329] 160.31 0.12 5.42 153.27 160.32 167.17 2082 1.00
## y_rep[330] 159.97 0.13 5.58 153.02 159.92 167.11 1819 1.00
## y_rep[331] 160.30 0.13 5.59 153.04 160.47 167.41 1934 1.00
## y_rep[332] 160.19 0.13 5.65 152.71 160.24 167.22 1979 1.00
## y_rep[333] 149.50 0.13 5.56 142.24 149.57 156.55 1954 1.00
## y_rep[334] 160.26 0.12 5.53 153.04 160.31 167.24 2136 1.00
## y_rep[335] 149.60 0.13 5.64 142.49 149.75 156.75 2001 1.00
## y_rep[336] 160.17 0.13 5.58 153.11 160.17 167.55 1831 1.00
## y_rep[337] 149.55 0.14 5.60 142.43 149.68 156.70 1607 1.00
## y_rep[338] 149.51 0.13 5.62 142.08 149.59 156.70 1970 1.00
## y_rep[339] 149.62 0.12 5.47 142.78 149.62 156.67 2217 1.00
## y_rep[340] 149.52 0.13 5.56 142.78 149.41 156.87 1947 1.00
## y_rep[341] 149.40 0.12 5.49 142.41 149.31 156.47 2024 1.00
## y_rep[342] 160.21 0.12 5.60 153.18 160.15 167.43 2083 1.00
## y_rep[343] 149.59 0.13 5.74 142.35 149.62 156.70 2076 1.00
## y_rep[344] 160.42 0.12 5.50 153.53 160.25 167.42 2095 1.00
## y_rep[345] 149.39 0.13 5.63 142.10 149.46 156.51 1931 1.00
## y_rep[346] 160.21 0.12 5.55 153.01 160.32 167.34 2044 1.00
## y_rep[347] 149.53 0.13 5.71 142.15 149.48 156.91 1867 1.00
## y_rep[348] 149.82 0.13 5.71 142.54 149.87 157.28 1963 1.00
## y_rep[349] 149.40 0.13 5.62 142.24 149.45 156.67 1982 1.00
## y_rep[350] 160.23 0.13 5.65 152.82 160.29 167.52 1857 1.00
## y_rep[351] 149.41 0.12 5.58 142.42 149.37 156.56 2084 1.00
## y_rep[352] 160.32 0.12 5.58 153.37 160.07 167.40 2011 1.00
## lp__ -782.25 0.06 1.24 -783.95 -781.93 -781.05 393 1.01
##
## Samples were drawn using NUTS(diag_e) at Fri Nov 22 15:25:48 2019.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).5 Polynomial regression
5.1 Howell 2: subset with only individuals over 18 years old
Standardizing the explanatory variable:
howell2 <- howell2 %>% mutate(weight.z = (weight - mean(weight)) / sd(weight))Data in a list:
m6.data <- list(N = nrow(howell2), height = howell2$height, weight = howell2$weight.z)data { // observed variables
int<lower=1> N; // number of observations
vector[N] height; // response variables
vector[N] weight; // predictor (previously centered)
}
parameters { // unobserved variables
real beta[3]; // parameters: intercept and slope
real sigma;
}
model {
height ~ normal(beta[1] + beta[2]*weight + beta[3]*(weight .* weight),sigma); // likelihood
beta[1] ~ normal(178, 100); // prior of the intercept
beta[2] ~ normal(0, 100); // prior of the slope
beta[3] ~ normal(0, 100);
sigma ~ uniform(0,50);
}
generated quantities {
vector[N] y_rep;
for(i in 1:N)
y_rep[i] = normal_rng(beta[1] + beta[2]*weight[i] + beta[3]*(weight[i] .* weight[i]), sigma);
}fit.m6 <- sampling(m6, data = m6.data, iter = 1000, chains = 4, cores = 4)
print(fit.m6, probs = c(0.10, 0.5, 0.9))## Inference for Stan model: c7fbeba14f23c52987bbbb1ee94a3a29.
## 4 chains, each with iter=1000; warmup=500; thin=1;
## post-warmup draws per chain=500, total post-warmup draws=2000.
##
## mean se_mean sd 10% 50% 90% n_eff Rhat
## beta[1] 154.60 0.01 0.36 154.16 154.60 155.06 1418 1.00
## beta[2] 5.86 0.01 0.27 5.51 5.86 6.20 469 1.01
## beta[3] -0.01 0.01 0.22 -0.30 -0.01 0.28 1421 1.00
## sigma 5.12 0.00 0.19 4.88 5.11 5.37 1951 1.00
## y_rep[1] 156.96 0.11 5.20 150.21 156.93 163.47 2056 1.00
## y_rep[2] 147.11 0.12 5.06 140.63 146.95 153.80 1768 1.00
## y_rep[3] 142.68 0.12 5.09 136.05 142.78 149.08 1912 1.00
## y_rep[4] 161.82 0.12 5.12 155.35 161.80 168.23 1837 1.00
## y_rep[5] 150.86 0.12 5.14 144.33 150.86 157.45 1960 1.00
## y_rep[6] 170.89 0.12 5.40 164.17 170.89 177.88 2034 1.00
## y_rep[7] 148.39 0.12 5.01 142.14 148.27 154.98 1658 1.00
## y_rep[8] 163.92 0.11 5.15 157.14 164.08 170.35 2110 1.00
## y_rep[9] 145.49 0.11 5.00 139.05 145.48 152.13 1918 1.00
## y_rep[10] 163.15 0.11 5.18 156.73 163.13 169.61 2070 1.00
## y_rep[11] 158.92 0.12 5.19 152.48 158.89 165.58 1990 1.00
## y_rep[12] 150.99 0.11 5.12 144.64 150.84 157.53 2035 1.00
## y_rep[13] 146.40 0.11 4.99 140.12 146.31 152.88 1978 1.00
## y_rep[14] 156.98 0.12 5.13 150.59 156.91 163.32 1945 1.00
## y_rep[15] 144.44 0.12 5.25 137.79 144.39 151.24 1907 1.00
## y_rep[16] 157.84 0.12 5.26 151.34 157.68 164.85 1873 1.00
## y_rep[17] 152.19 0.11 5.14 145.74 152.13 158.73 2086 1.00
## y_rep[18] 148.45 0.12 5.31 141.64 148.36 155.35 2009 1.00
## y_rep[19] 158.21 0.11 5.07 151.85 158.30 164.68 2052 1.00
## y_rep[20] 152.70 0.12 5.10 146.16 152.72 159.11 1901 1.00
## y_rep[21] 145.96 0.12 5.17 139.18 146.05 152.52 1737 1.00
## y_rep[22] 148.11 0.11 5.23 141.44 148.18 154.60 2070 1.00
## y_rep[23] 145.87 0.12 5.07 139.27 145.81 152.32 1839 1.00
## y_rep[24] 150.47 0.11 5.18 143.79 150.53 157.11 2039 1.00
## y_rep[25] 163.75 0.11 5.02 157.31 163.77 170.14 2065 1.00
## y_rep[26] 148.04 0.12 5.20 141.46 148.07 154.90 2001 1.00
## y_rep[27] 148.57 0.11 5.06 141.96 148.51 155.05 1998 1.00
## y_rep[28] 155.99 0.11 5.19 149.44 155.92 162.81 2201 1.00
## y_rep[29] 148.92 0.12 5.06 142.40 148.95 155.35 1889 1.00
## y_rep[30] 146.05 0.11 5.09 139.68 145.96 152.63 2089 1.00
## y_rep[31] 156.79 0.11 5.11 150.45 156.68 163.49 2039 1.00
## y_rep[32] 157.19 0.12 5.15 150.49 157.24 163.64 1927 1.00
## y_rep[33] 158.62 0.11 5.00 152.17 158.63 164.98 2029 1.00
## y_rep[34] 158.63 0.11 5.04 152.09 158.65 165.11 2043 1.00
## y_rep[35] 165.21 0.12 5.21 158.61 165.26 172.11 1976 1.00
## y_rep[36] 149.40 0.12 5.01 142.77 149.37 155.93 1832 1.00
## y_rep[37] 159.05 0.11 5.16 152.34 159.06 165.79 2099 1.00
## y_rep[38] 151.07 0.11 5.19 144.59 150.92 157.83 2169 1.00
## y_rep[39] 148.84 0.12 5.07 142.29 148.78 155.47 1915 1.00
## y_rep[40] 152.16 0.11 5.02 145.87 152.03 158.70 2008 1.00
## y_rep[41] 154.28 0.12 5.25 147.52 154.28 160.79 2079 1.00
## y_rep[42] 166.83 0.12 5.32 159.95 166.90 173.46 1930 1.00
## y_rep[43] 156.14 0.11 5.19 149.57 156.08 162.90 2045 1.00
## y_rep[44] 153.85 0.11 5.14 147.45 153.90 160.43 2126 1.00
## y_rep[45] 160.00 0.12 5.15 153.31 160.16 166.46 1905 1.00
## y_rep[46] 163.00 0.10 4.91 156.62 162.96 169.28 2227 1.00
## y_rep[47] 155.36 0.12 5.11 148.55 155.34 161.75 1789 1.00
## y_rep[48] 157.51 0.11 5.05 151.27 157.36 163.92 2036 1.00
## y_rep[49] 161.09 0.12 4.98 154.87 161.09 167.53 1805 1.00
## y_rep[50] 156.89 0.11 5.17 150.22 156.76 163.59 2086 1.00
## y_rep[51] 155.18 0.12 5.10 148.78 155.07 161.78 1894 1.00
## y_rep[52] 152.13 0.12 5.19 145.59 152.17 158.76 1896 1.00
## y_rep[53] 146.81 0.12 5.12 140.24 146.84 153.34 1970 1.00
## y_rep[54] 164.54 0.11 5.07 158.08 164.45 171.03 2024 1.00
## y_rep[55] 147.55 0.11 4.99 141.23 147.50 153.99 2034 1.00
## y_rep[56] 157.54 0.11 5.03 150.96 157.53 163.99 2123 1.00
## y_rep[57] 147.72 0.12 5.02 141.31 147.68 154.08 1803 1.00
## y_rep[58] 156.62 0.11 5.03 150.20 156.69 163.05 2055 1.00
## y_rep[59] 156.65 0.11 5.05 150.33 156.52 163.09 2087 1.00
## y_rep[60] 165.93 0.11 5.28 159.32 165.83 172.71 2108 1.00
## y_rep[61] 148.15 0.12 5.26 141.61 148.11 154.83 2088 1.00
## y_rep[62] 156.57 0.12 5.18 150.13 156.53 163.20 1918 1.00
## y_rep[63] 152.80 0.12 5.04 146.28 152.92 159.17 1904 1.00
## y_rep[64] 159.33 0.12 5.15 152.68 159.30 165.78 1885 1.00
## y_rep[65] 149.37 0.11 5.07 142.87 149.34 155.75 2005 1.00
## y_rep[66] 159.60 0.11 5.17 153.00 159.61 166.33 2035 1.00
## y_rep[67] 149.78 0.12 5.34 142.96 149.92 156.46 2079 1.00
## y_rep[68] 146.69 0.12 5.02 140.22 146.64 153.13 1679 1.00
## y_rep[69] 155.69 0.11 5.08 148.98 155.71 162.27 2049 1.00
## y_rep[70] 152.34 0.12 5.26 145.56 152.32 159.02 1853 1.00
## y_rep[71] 157.21 0.11 4.99 151.15 157.06 163.66 2007 1.00
## y_rep[72] 164.37 0.12 5.15 157.83 164.26 171.10 1927 1.00
## y_rep[73] 157.91 0.12 5.15 151.36 157.81 164.42 1822 1.00
## y_rep[74] 152.64 0.11 5.09 146.18 152.59 159.16 2126 1.00
## y_rep[75] 145.58 0.11 5.11 139.16 145.50 152.21 1993 1.00
## y_rep[76] 165.24 0.12 5.23 158.52 165.32 172.02 2007 1.00
## y_rep[77] 160.08 0.11 5.12 153.48 159.94 166.74 2010 1.00
## y_rep[78] 156.67 0.12 5.17 150.15 156.66 163.15 1836 1.00
## y_rep[79] 151.12 0.11 5.08 144.74 151.06 157.61 2004 1.00
## y_rep[80] 143.58 0.12 5.09 137.16 143.50 150.13 1918 1.00
## y_rep[81] 165.34 0.13 5.29 158.53 165.32 171.96 1732 1.00
## y_rep[82] 152.78 0.12 5.11 146.60 152.62 159.14 1950 1.00
## y_rep[83] 150.18 0.12 5.14 143.60 150.04 157.04 1841 1.00
## y_rep[84] 155.69 0.11 5.08 149.38 155.69 162.26 2017 1.00
## y_rep[85] 151.09 0.12 5.07 144.59 151.02 157.48 1855 1.00
## y_rep[86] 157.00 0.12 5.19 150.33 156.96 163.71 1868 1.00
## y_rep[87] 147.79 0.12 5.23 141.19 147.88 154.46 1980 1.00
## y_rep[88] 154.55 0.12 5.25 147.95 154.51 161.07 1994 1.00
## y_rep[89] 151.91 0.12 5.15 145.45 151.89 158.69 1980 1.00
## y_rep[90] 163.55 0.11 5.13 156.95 163.59 170.06 2126 1.00
## y_rep[91] 162.47 0.11 5.12 156.13 162.33 169.18 2134 1.00
## y_rep[92] 161.14 0.12 5.10 154.58 161.04 167.99 1927 1.00
## y_rep[93] 152.15 0.12 5.18 145.50 152.00 158.90 1925 1.00
## y_rep[94] 158.69 0.11 5.07 151.95 158.74 165.03 2012 1.00
## y_rep[95] 151.62 0.12 5.08 145.09 151.75 158.13 1944 1.00
## y_rep[96] 164.62 0.12 5.24 157.82 164.61 171.40 2009 1.00
## y_rep[97] 152.20 0.12 5.24 145.43 152.13 158.88 1860 1.00
## y_rep[98] 162.04 0.12 5.17 155.39 162.04 168.46 1879 1.00
## y_rep[99] 159.37 0.12 5.25 152.39 159.40 165.83 1980 1.00
## y_rep[100] 152.33 0.11 5.08 145.82 152.35 158.86 1953 1.00
## y_rep[101] 158.31 0.11 5.07 152.00 158.19 164.93 1992 1.00
## y_rep[102] 148.71 0.11 5.08 142.06 148.77 155.20 2134 1.00
## y_rep[103] 158.91 0.11 5.06 152.45 158.85 165.69 2006 1.00
## y_rep[104] 167.83 0.13 5.24 161.30 167.85 174.52 1728 1.00
## y_rep[105] 157.08 0.12 5.06 150.62 157.12 163.56 1932 1.00
## y_rep[106] 149.22 0.11 5.06 142.61 149.34 155.58 2095 1.00
## y_rep[107] 147.09 0.11 5.10 140.47 147.08 153.56 2177 1.00
## y_rep[108] 151.98 0.12 5.11 145.60 151.98 158.57 1957 1.00
## y_rep[109] 154.16 0.11 5.21 147.70 154.23 160.57 2167 1.00
## y_rep[110] 157.26 0.11 5.08 150.65 157.35 163.63 2012 1.00
## y_rep[111] 163.87 0.11 5.12 157.32 163.96 170.45 2074 1.00
## y_rep[112] 143.87 0.12 5.21 137.06 143.87 150.55 2018 1.00
## y_rep[113] 150.89 0.12 5.24 144.30 150.94 157.65 1992 1.00
## y_rep[114] 160.28 0.12 5.14 153.85 160.30 166.70 1964 1.00
## y_rep[115] 158.13 0.12 5.12 151.70 158.07 164.58 1874 1.00
## y_rep[116] 162.20 0.12 5.12 155.57 162.31 168.60 1746 1.00
## y_rep[117] 162.79 0.13 5.25 155.94 162.98 169.45 1752 1.00
## y_rep[118] 163.97 0.12 5.17 157.31 164.00 170.60 1868 1.00
## y_rep[119] 152.08 0.12 5.16 145.45 151.95 158.55 2011 1.00
## y_rep[120] 150.96 0.12 5.12 144.27 150.98 157.52 1970 1.00
## y_rep[121] 158.61 0.12 5.15 151.82 158.59 165.30 1892 1.00
## y_rep[122] 154.12 0.11 5.07 147.48 154.18 160.72 1983 1.00
## y_rep[123] 155.46 0.12 5.16 148.64 155.50 162.10 1762 1.00
## y_rep[124] 151.67 0.13 5.22 145.00 151.55 158.36 1662 1.00
## y_rep[125] 160.49 0.11 5.01 154.15 160.45 167.07 1962 1.00
## y_rep[126] 153.94 0.12 5.23 147.45 154.02 160.54 2014 1.00
## y_rep[127] 142.89 0.12 5.21 136.26 142.94 149.50 1949 1.00
## y_rep[128] 165.04 0.12 5.17 158.45 165.09 171.34 1928 1.00
## y_rep[129] 161.60 0.12 5.21 154.86 161.56 168.20 1922 1.00
## y_rep[130] 146.82 0.12 5.25 140.05 147.02 153.45 1907 1.00
## y_rep[131] 158.14 0.13 5.20 151.34 158.05 164.74 1686 1.00
## y_rep[132] 165.29 0.12 5.15 158.68 165.32 171.99 1823 1.00
## y_rep[133] 152.17 0.11 5.20 145.51 152.15 158.71 2147 1.00
## y_rep[134] 159.36 0.12 5.19 152.61 159.30 166.09 1740 1.00
## y_rep[135] 156.23 0.11 5.08 149.91 156.13 162.56 2011 1.00
## y_rep[136] 169.63 0.12 5.30 162.69 169.70 176.25 1888 1.00
## y_rep[137] 158.52 0.11 5.03 151.91 158.60 164.99 2037 1.00
## y_rep[138] 142.39 0.11 5.14 135.71 142.38 149.20 2029 1.00
## y_rep[139] 145.64 0.11 5.17 139.19 145.57 152.22 2101 1.00
## y_rep[140] 155.09 0.12 4.98 148.81 155.05 161.49 1789 1.00
## y_rep[141] 153.84 0.13 5.20 147.21 153.73 160.67 1708 1.00
## y_rep[142] 155.10 0.12 5.18 148.28 155.32 161.87 1904 1.00
## y_rep[143] 149.30 0.15 5.13 142.91 149.32 155.83 1206 1.00
## y_rep[144] 150.94 0.11 5.00 144.52 150.87 157.33 1901 1.00
## y_rep[145] 154.86 0.11 5.11 148.34 154.84 161.33 2107 1.00
## y_rep[146] 162.61 0.12 5.27 155.89 162.61 169.35 1913 1.00
## y_rep[147] 161.24 0.12 5.15 154.51 161.16 167.91 1866 1.00
## y_rep[148] 149.25 0.11 5.15 142.54 149.26 155.82 2054 1.00
## y_rep[149] 155.13 0.11 5.15 148.60 155.23 161.80 2042 1.00
## y_rep[150] 150.41 0.11 5.04 144.14 150.34 156.89 1977 1.00
## y_rep[151] 160.60 0.12 5.02 153.95 160.65 167.13 1904 1.00
## y_rep[152] 148.95 0.12 5.19 142.40 148.94 155.38 2025 1.00
## y_rep[153] 149.40 0.11 5.14 142.87 149.50 155.99 1999 1.00
## y_rep[154] 153.86 0.12 5.17 147.19 153.85 160.59 1880 1.00
## y_rep[155] 149.86 0.13 5.25 143.22 149.87 156.64 1620 1.00
## y_rep[156] 141.82 0.12 5.17 135.27 141.88 148.46 1954 1.00
## y_rep[157] 156.20 0.12 5.09 149.56 156.15 162.79 1927 1.00
## y_rep[158] 150.59 0.11 4.96 144.03 150.52 156.86 1989 1.00
## y_rep[159] 159.29 0.11 5.02 152.85 159.26 165.78 2038 1.00
## y_rep[160] 151.13 0.12 5.12 144.58 151.02 157.80 1724 1.00
## y_rep[161] 163.22 0.12 5.14 156.58 163.40 169.77 1788 1.00
## y_rep[162] 154.74 0.12 5.08 147.99 154.80 161.23 1783 1.00
## y_rep[163] 146.22 0.13 5.20 139.38 146.29 152.75 1661 1.00
## y_rep[164] 154.84 0.12 5.20 148.11 154.74 161.47 1976 1.00
## y_rep[165] 157.37 0.11 5.09 150.97 157.39 163.75 2089 1.00
## y_rep[166] 155.13 0.12 5.17 148.27 155.18 161.84 1913 1.00
## y_rep[167] 157.50 0.12 5.16 150.91 157.58 164.09 1880 1.00
## y_rep[168] 151.07 0.12 5.24 144.04 151.08 157.66 2000 1.00
## y_rep[169] 148.75 0.11 4.99 142.25 148.79 155.01 2039 1.00
## y_rep[170] 152.06 0.12 5.11 145.65 151.83 158.58 1912 1.00
## y_rep[171] 148.72 0.12 5.22 142.20 148.80 155.38 1995 1.00
## y_rep[172] 157.52 0.11 5.11 151.18 157.49 164.12 2007 1.00
## y_rep[173] 149.02 0.12 5.16 142.51 148.92 155.66 2001 1.00
## y_rep[174] 150.09 0.12 5.04 143.69 149.96 156.73 1700 1.00
## y_rep[175] 159.24 0.11 4.92 152.71 159.33 165.57 2008 1.00
## y_rep[176] 162.93 0.12 5.05 156.55 163.14 169.21 1918 1.00
## y_rep[177] 154.97 0.11 5.28 148.24 155.03 161.58 2144 1.00
## y_rep[178] 149.68 0.12 5.25 142.92 149.62 156.29 1791 1.00
## y_rep[179] 152.75 0.12 5.28 146.07 152.68 159.51 1995 1.00
## y_rep[180] 142.56 0.12 5.33 135.57 142.57 149.48 1821 1.00
## y_rep[181] 155.13 0.11 5.09 148.65 155.03 161.68 1997 1.00
## y_rep[182] 148.35 0.12 5.20 141.58 148.45 154.85 2021 1.00
## y_rep[183] 146.44 0.12 5.14 139.92 146.42 152.87 1859 1.00
## y_rep[184] 151.02 0.12 5.07 144.49 151.06 157.54 1917 1.00
## y_rep[185] 157.17 0.12 5.12 150.52 157.26 163.63 1892 1.00
## y_rep[186] 157.01 0.12 5.14 150.64 157.11 163.34 1811 1.00
## y_rep[187] 155.91 0.12 5.15 149.14 156.00 162.46 1838 1.00
## y_rep[188] 151.15 0.11 5.11 144.60 151.25 157.67 2153 1.00
## y_rep[189] 146.98 0.12 5.06 140.12 147.03 153.16 1911 1.00
## y_rep[190] 157.29 0.13 5.10 150.55 157.39 163.70 1520 1.00
## y_rep[191] 147.07 0.12 5.13 140.61 147.05 153.64 1978 1.00
## y_rep[192] 164.78 0.12 5.25 158.04 164.87 171.53 2041 1.00
## y_rep[193] 149.01 0.12 5.13 142.51 148.97 155.65 1925 1.00
## y_rep[194] 156.86 0.12 5.27 149.95 156.96 163.59 1927 1.00
## y_rep[195] 146.75 0.13 5.20 140.15 146.68 153.32 1715 1.00
## y_rep[196] 151.38 0.12 5.13 144.66 151.47 157.95 1977 1.00
## y_rep[197] 154.55 0.12 5.17 147.91 154.60 161.12 1985 1.00
## y_rep[198] 159.47 0.12 5.19 152.55 159.62 166.02 1820 1.00
## y_rep[199] 164.04 0.11 5.14 157.85 163.93 170.47 2042 1.00
## y_rep[200] 148.16 0.11 5.05 141.63 148.30 154.63 1931 1.00
## y_rep[201] 166.64 0.12 5.24 159.98 166.68 173.24 1966 1.00
## y_rep[202] 154.26 0.11 5.06 147.89 154.26 160.68 1940 1.00
## y_rep[203] 153.97 0.12 5.23 147.28 154.02 160.68 1934 1.00
## y_rep[204] 154.09 0.13 5.10 147.38 154.15 160.31 1595 1.00
## y_rep[205] 154.10 0.12 5.17 147.37 154.14 160.74 1992 1.00
## y_rep[206] 150.49 0.11 5.09 144.16 150.44 157.25 2074 1.00
## y_rep[207] 153.74 0.11 5.06 147.23 153.78 160.42 1976 1.00
## y_rep[208] 144.94 0.13 5.23 138.48 144.76 151.72 1593 1.00
## y_rep[209] 143.48 0.13 5.19 136.98 143.34 150.15 1654 1.00
## y_rep[210] 146.36 0.12 5.18 139.77 146.41 152.82 1997 1.00
## y_rep[211] 158.77 0.12 5.18 152.23 158.91 165.43 1847 1.00
## y_rep[212] 161.92 0.12 5.05 155.34 161.97 168.42 1823 1.00
## y_rep[213] 147.38 0.11 5.23 140.48 147.51 154.06 2113 1.00
## y_rep[214] 150.57 0.11 5.13 144.04 150.57 157.19 2004 1.00
## y_rep[215] 159.73 0.11 4.93 153.15 159.83 166.01 1921 1.00
## y_rep[216] 153.68 0.12 5.18 147.07 153.73 160.41 1861 1.00
## y_rep[217] 158.96 0.12 5.15 152.46 158.93 165.69 1752 1.00
## y_rep[218] 144.38 0.11 5.22 137.80 144.50 151.08 2121 1.00
## y_rep[219] 153.54 0.12 5.13 146.80 153.65 160.03 1936 1.00
## y_rep[220] 157.49 0.12 5.19 150.82 157.67 164.12 1996 1.00
## y_rep[221] 152.78 0.12 5.12 146.35 152.70 159.57 1933 1.00
## y_rep[222] 144.66 0.12 5.20 138.22 144.62 151.36 1979 1.00
## y_rep[223] 149.83 0.12 5.18 143.03 150.07 156.56 1823 1.00
## y_rep[224] 146.20 0.11 5.07 139.64 146.25 152.62 2118 1.00
## y_rep[225] 160.02 0.12 5.09 153.43 159.97 166.44 1809 1.00
## y_rep[226] 155.23 0.11 5.15 148.59 155.22 161.84 2032 1.00
## y_rep[227] 158.21 0.11 5.22 151.31 158.29 164.92 2080 1.00
## y_rep[228] 167.11 0.12 5.19 160.68 166.90 173.85 1763 1.00
## y_rep[229] 153.46 0.12 5.17 146.98 153.42 160.04 1772 1.00
## y_rep[230] 161.04 0.11 5.21 154.30 160.98 167.69 2188 1.00
## y_rep[231] 159.84 0.12 5.04 153.16 160.07 166.23 1882 1.00
## y_rep[232] 144.86 0.11 5.08 138.29 144.80 151.38 1972 1.00
## y_rep[233] 149.45 0.11 5.09 143.03 149.44 155.82 1997 1.00
## y_rep[234] 167.68 0.12 5.36 160.84 167.60 174.66 2134 1.00
## y_rep[235] 161.02 0.12 5.25 154.41 161.05 167.74 1937 1.00
## y_rep[236] 150.03 0.12 5.12 143.58 149.94 156.66 1971 1.00
## y_rep[237] 153.71 0.11 5.10 147.40 153.61 160.28 1997 1.00
## y_rep[238] 163.29 0.11 5.13 156.58 163.43 169.89 2030 1.00
## y_rep[239] 154.74 0.12 5.20 148.10 154.61 161.56 1947 1.00
## y_rep[240] 151.20 0.12 5.18 144.64 151.22 157.75 1925 1.00
## y_rep[241] 151.54 0.12 5.17 144.98 151.43 158.21 1943 1.00
## y_rep[242] 152.41 0.11 5.04 146.04 152.29 158.93 2087 1.00
## y_rep[243] 152.94 0.11 5.01 146.78 152.85 159.29 2023 1.00
## y_rep[244] 150.85 0.11 5.09 144.28 150.99 157.50 2100 1.00
## y_rep[245] 152.94 0.12 5.26 146.16 152.85 159.76 1983 1.00
## y_rep[246] 155.72 0.12 5.28 148.91 155.78 162.31 1979 1.00
## y_rep[247] 157.09 0.11 5.06 150.56 157.12 163.49 2042 1.00
## y_rep[248] 152.35 0.12 5.21 145.83 152.38 158.97 1890 1.00
## y_rep[249] 157.76 0.12 5.18 151.11 157.69 164.52 1916 1.00
## y_rep[250] 155.46 0.12 5.08 149.06 155.53 161.70 1830 1.00
## y_rep[251] 161.73 0.12 5.20 154.96 161.80 168.36 1951 1.00
## y_rep[252] 156.93 0.12 5.11 150.42 156.89 163.45 1784 1.00
## y_rep[253] 153.44 0.11 5.01 146.91 153.40 160.05 2083 1.00
## y_rep[254] 153.16 0.11 5.07 146.57 153.25 159.37 1948 1.00
## y_rep[255] 161.84 0.11 5.13 155.21 161.73 168.39 2020 1.00
## y_rep[256] 154.57 0.12 5.29 147.88 154.50 161.46 1835 1.00
## y_rep[257] 156.59 0.12 5.13 150.07 156.75 163.03 1953 1.00
## y_rep[258] 142.51 0.13 5.32 135.75 142.49 149.22 1667 1.00
## y_rep[259] 164.74 0.12 5.19 157.94 164.86 171.16 1894 1.00
## y_rep[260] 164.47 0.11 5.08 158.03 164.47 170.87 1980 1.00
## y_rep[261] 157.17 0.12 5.17 150.79 157.09 163.75 1935 1.00
## y_rep[262] 154.37 0.11 5.06 147.73 154.39 160.93 2076 1.00
## y_rep[263] 155.00 0.11 5.12 148.62 155.00 161.58 1987 1.00
## y_rep[264] 158.11 0.12 5.11 151.60 158.11 164.64 1791 1.00
## y_rep[265] 156.03 0.11 5.09 149.44 155.96 162.31 1961 1.00
## y_rep[266] 153.42 0.12 5.18 146.63 153.52 160.00 1820 1.00
## y_rep[267] 164.64 0.12 5.20 157.78 164.67 171.35 2038 1.00
## y_rep[268] 150.26 0.12 5.12 143.67 150.20 156.91 1933 1.00
## y_rep[269] 160.13 0.11 5.01 153.65 160.11 166.37 1962 1.00
## y_rep[270] 155.73 0.12 5.09 149.21 155.84 162.11 1958 1.00
## y_rep[271] 158.33 0.13 5.13 151.85 158.37 164.99 1684 1.00
## y_rep[272] 153.91 0.12 5.06 147.45 153.84 160.60 1718 1.00
## y_rep[273] 160.20 0.12 5.10 153.66 160.19 166.77 1931 1.00
## y_rep[274] 150.66 0.12 5.23 144.02 150.59 157.36 2064 1.00
## y_rep[275] 147.61 0.11 5.13 140.98 147.71 154.22 2031 1.00
## y_rep[276] 160.59 0.12 5.10 154.02 160.60 167.07 1791 1.00
## y_rep[277] 154.34 0.12 5.14 147.87 154.37 160.79 1870 1.00
## y_rep[278] 153.17 0.12 5.19 146.58 153.14 159.78 1937 1.00
## y_rep[279] 155.99 0.12 5.18 149.41 156.01 162.86 1828 1.00
## y_rep[280] 149.67 0.11 4.99 143.32 149.73 155.98 1935 1.00
## y_rep[281] 145.42 0.12 5.11 138.90 145.44 152.00 1919 1.00
## y_rep[282] 149.49 0.11 5.14 142.76 149.41 156.24 2103 1.00
## y_rep[283] 147.80 0.14 5.12 141.18 147.74 154.48 1338 1.00
## y_rep[284] 157.74 0.13 5.33 150.97 157.87 164.48 1808 1.00
## y_rep[285] 146.25 0.12 5.04 139.67 146.35 152.59 1721 1.00
## y_rep[286] 153.48 0.12 5.12 146.83 153.45 159.91 1810 1.00
## y_rep[287] 157.52 0.11 5.24 150.84 157.42 164.11 2248 1.00
## y_rep[288] 160.10 0.11 5.01 153.83 160.13 166.35 1971 1.00
## y_rep[289] 153.83 0.11 5.10 147.46 153.73 160.38 2030 1.00
## y_rep[290] 157.45 0.11 5.06 151.02 157.40 163.97 2290 1.00
## y_rep[291] 156.19 0.12 5.20 149.57 156.21 162.92 1899 1.00
## y_rep[292] 165.03 0.12 5.12 158.55 165.08 171.55 1877 1.00
## y_rep[293] 157.84 0.11 5.11 151.39 157.62 164.46 2009 1.00
## y_rep[294] 157.69 0.11 5.03 151.25 157.80 164.08 2081 1.00
## y_rep[295] 156.93 0.11 5.01 150.51 156.86 163.24 2156 1.00
## y_rep[296] 146.00 0.12 5.23 139.56 146.02 152.80 1934 1.00
## y_rep[297] 147.02 0.11 5.00 140.61 147.02 153.34 1937 1.00
## y_rep[298] 158.23 0.11 5.03 151.61 158.25 164.74 1990 1.00
## y_rep[299] 160.19 0.12 5.03 153.86 160.13 166.75 1867 1.00
## y_rep[300] 156.12 0.12 5.28 149.35 155.94 162.87 1980 1.00
## y_rep[301] 147.35 0.12 5.09 140.91 147.28 153.80 1745 1.00
## y_rep[302] 157.90 0.12 5.17 151.32 157.86 164.67 1970 1.00
## y_rep[303] 148.32 0.11 5.10 141.94 148.33 155.12 2059 1.00
## y_rep[304] 156.74 0.11 5.15 150.02 156.77 163.58 2094 1.00
## y_rep[305] 164.10 0.12 5.25 157.22 164.10 170.65 1855 1.00
## y_rep[306] 163.00 0.11 5.11 156.58 163.00 169.65 2052 1.00
## y_rep[307] 157.85 0.11 5.06 151.22 157.93 164.37 1948 1.00
## y_rep[308] 152.83 0.12 5.10 146.18 152.75 159.32 1918 1.00
## y_rep[309] 144.68 0.12 5.23 137.79 144.74 151.16 1920 1.00
## y_rep[310] 159.14 0.12 5.20 152.48 159.14 165.96 1928 1.00
## y_rep[311] 153.84 0.12 5.24 147.02 153.92 160.35 2030 1.00
## y_rep[312] 144.27 0.12 5.21 137.92 144.31 150.94 1946 1.00
## y_rep[313] 156.65 0.12 5.12 150.26 156.64 163.06 1751 1.00
## y_rep[314] 155.51 0.13 5.25 148.81 155.57 161.91 1537 1.00
## y_rep[315] 156.68 0.12 5.16 150.20 156.70 163.10 1864 1.00
## y_rep[316] 150.78 0.11 5.26 144.09 150.68 157.39 2232 1.00
## y_rep[317] 159.47 0.12 5.15 153.03 159.48 166.01 1851 1.00
## y_rep[318] 154.77 0.11 5.20 147.97 154.82 161.31 2227 1.00
## y_rep[319] 152.02 0.11 5.11 145.46 151.99 158.52 2026 1.00
## y_rep[320] 151.67 0.11 5.13 145.06 151.69 158.23 2106 1.00
## y_rep[321] 154.57 0.11 5.14 148.08 154.50 161.21 2133 1.00
## y_rep[322] 160.15 0.11 5.14 153.60 160.05 166.75 2021 1.00
## y_rep[323] 158.42 0.11 5.09 151.92 158.47 164.89 2025 1.00
## y_rep[324] 160.25 0.12 5.25 153.31 160.32 166.86 2022 1.00
## y_rep[325] 153.62 0.12 5.15 146.99 153.59 160.12 1979 1.00
## y_rep[326] 146.11 0.12 4.99 139.81 146.12 152.34 1861 1.00
## y_rep[327] 152.53 0.12 5.06 145.97 152.51 159.03 1699 1.00
## y_rep[328] 156.49 0.12 5.21 149.71 156.43 163.16 2035 1.00
## y_rep[329] 151.66 0.12 5.07 145.26 151.64 158.19 1887 1.00
## y_rep[330] 148.41 0.11 5.04 141.88 148.47 154.86 2041 1.00
## y_rep[331] 153.13 0.11 5.25 146.36 153.18 159.83 2084 1.00
## y_rep[332] 162.26 0.12 5.05 155.56 162.38 168.67 1836 1.00
## y_rep[333] 152.71 0.11 5.19 146.05 152.73 159.43 2124 1.00
## y_rep[334] 149.88 0.11 5.04 143.40 149.90 156.23 2053 1.00
## y_rep[335] 153.14 0.12 5.13 146.70 153.16 159.64 1945 1.00
## y_rep[336] 161.66 0.11 5.05 155.10 161.81 168.03 2212 1.00
## y_rep[337] 148.89 0.12 5.10 142.28 148.90 155.46 1936 1.00
## y_rep[338] 152.65 0.12 5.02 146.29 152.75 158.96 1869 1.00
## y_rep[339] 146.29 0.12 5.06 139.85 146.20 152.87 1915 1.00
## y_rep[340] 153.75 0.12 5.11 147.21 153.76 160.27 1804 1.00
## y_rep[341] 148.39 0.11 5.10 141.82 148.42 154.75 1998 1.00
## y_rep[342] 154.01 0.11 5.24 147.44 153.88 160.72 2117 1.00
## y_rep[343] 153.83 0.12 5.24 147.17 153.81 160.46 1972 1.00
## y_rep[344] 157.35 0.12 5.09 150.88 157.26 164.11 1894 1.00
## y_rep[345] 149.50 0.11 5.17 142.71 149.62 156.02 2078 1.00
## y_rep[346] 151.02 0.11 5.11 144.54 150.94 157.75 2151 1.00
## y_rep[347] 150.94 0.12 5.23 144.33 150.89 157.65 1849 1.00
## y_rep[348] 156.21 0.12 5.09 149.57 156.42 162.70 1795 1.00
## y_rep[349] 145.00 0.11 5.19 138.38 144.94 151.72 2052 1.00
## y_rep[350] 160.97 0.12 5.25 154.15 160.99 167.66 1988 1.00
## y_rep[351] 162.93 0.11 5.09 156.41 162.97 169.60 2032 1.00
## y_rep[352] 161.19 0.12 5.14 154.59 161.20 167.91 1942 1.00
## lp__ -749.55 0.05 1.39 -751.40 -749.20 -748.11 818 1.00
##
## Samples were drawn using NUTS(diag_e) at Fri Nov 22 15:25:51 2019.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).summary(lm(height~weight.z+I(weight.z^2),data=howell2))##
## Call:
## lm(formula = height ~ weight.z + I(weight.z^2), data = howell2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -19.7517 -2.8933 0.0313 3.1419 14.7936
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 154.60953 0.35209 439.120 <2e-16 ***
## weight.z 5.84515 0.27348 21.373 <2e-16 ***
## I(weight.z^2) -0.01248 0.22483 -0.055 0.956
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.094 on 349 degrees of freedom
## Multiple R-squared: 0.5696, Adjusted R-squared: 0.5672
## F-statistic: 231 on 2 and 349 DF, p-value: < 2.2e-16See Figure 4.9 of Statistical rethinking
https://github.com/ssp3nc3r/rethinking/blob/master/chapter04.Rmd
Here, all the variance is represented (variance of actual heights).
5.2 Howell 1: data set with all individuals
Standardizing the explanatory variable:
howell1 <- howell1 %>% mutate(weight.z = (weight - mean(weight)) / sd(weight))Data in a list:
m7.data <- list(N = nrow(howell1), height = howell1$height, weight = howell1$weight.z)data { // observed variables
int<lower=1> N; // number of observations
vector[N] height; // response variables
vector[N] weight; // predictor (previously centered)
}
parameters { // unobserved variables
real beta[3]; // parameters: intercept and slope
real sigma;
}
model {
height ~ normal(beta[1] + beta[2]*weight + beta[3]*(weight .* weight),sigma); // likelihood
beta[1] ~ normal(178, 100); // prior of the intercept
beta[2] ~ normal(0, 100); // prior of the slope
beta[3] ~ normal(0, 100);
sigma ~ uniform(0,50);
}
generated quantities {
vector[N] y_rep;
for(i in 1:N)
y_rep[i] = normal_rng(beta[1] + beta[2]*weight[i] + beta[3]*(weight[i] .* weight[i]), sigma);
}fit.m7 <- sampling(m7, data = m7.data, iter = 1000, chains = 4, cores = 4)
print(fit.m7, probs = c(0.10, 0.5, 0.9))## Inference for Stan model: c7fbeba14f23c52987bbbb1ee94a3a29.
## 4 chains, each with iter=1000; warmup=500; thin=1;
## post-warmup draws per chain=500, total post-warmup draws=2000.
##
## mean se_mean sd 10% 50% 90% n_eff Rhat
## beta[1] 146.65 0.01 0.37 146.15 146.65 147.10 833 1
## beta[2] 21.44 0.01 0.29 21.07 21.44 21.80 870 1
## beta[3] -8.40 0.01 0.28 -8.77 -8.40 -8.05 777 1
## sigma 5.78 0.00 0.17 5.56 5.77 6.00 2177 1
## y_rep[1] 158.64 0.13 5.86 151.00 158.69 166.23 1904 1
## y_rep[2] 148.05 0.13 5.81 140.84 148.13 155.35 1983 1
## y_rep[3] 140.88 0.14 5.79 133.32 141.07 148.17 1797 1
## y_rep[4] 160.30 0.13 5.80 152.89 160.17 167.85 2078 1
## y_rep[5] 153.69 0.12 5.68 146.41 153.66 160.99 2115 1
## y_rep[6] 157.73 0.13 5.89 150.08 157.84 165.16 2038 1
## y_rep[7] 150.28 0.14 5.78 142.99 150.27 157.62 1710 1
## y_rep[8] 160.28 0.12 5.77 152.93 160.23 167.86 2168 1
## y_rep[9] 145.26 0.13 5.82 137.66 145.14 152.78 2073 1
## y_rep[10] 160.44 0.13 5.69 153.14 160.57 167.72 1806 1
## y_rep[11] 159.60 0.13 5.78 152.26 159.60 166.99 1897 1
## y_rep[12] 153.32 0.14 5.96 145.52 153.34 161.03 1813 1
## y_rep[13] 147.17 0.13 5.76 140.08 146.93 154.52 1992 1
## y_rep[14] 158.55 0.14 5.72 151.15 158.57 165.96 1718 1
## y_rep[15] 143.84 0.14 5.81 136.50 143.88 151.18 1750 1
## y_rep[16] 159.17 0.14 5.71 151.89 159.20 166.68 1757 1
## y_rep[17] 154.68 0.13 5.69 147.25 154.56 161.92 2050 1
## y_rep[18] 150.12 0.13 5.85 142.49 150.16 157.60 1958 1
## y_rep[19] 113.18 0.13 5.72 105.84 113.17 120.34 2000 1
## y_rep[20] 97.15 0.14 5.93 89.53 97.17 104.48 1919 1
## y_rep[21] 85.50 0.13 5.85 77.92 85.67 92.78 1887 1
## y_rep[22] 159.26 0.13 5.77 151.70 159.43 166.55 2035 1
## y_rep[23] 154.97 0.14 5.80 147.01 155.11 162.45 1767 1
## y_rep[24] 123.59 0.14 5.87 115.96 123.49 131.31 1879 1
## y_rep[25] 103.14 0.13 5.75 95.71 102.99 110.73 2022 1
## y_rep[26] 146.28 0.14 5.80 138.99 146.19 153.60 1844 1
## y_rep[27] 149.85 0.13 5.83 142.37 149.95 157.30 1878 1
## y_rep[28] 146.66 0.13 5.66 139.26 146.70 153.97 1956 1
## y_rep[29] 131.94 0.13 5.87 124.54 131.99 139.47 1984 1
## y_rep[30] 121.47 0.13 5.78 114.12 121.41 128.89 1927 1
## y_rep[31] 108.69 0.13 5.89 101.29 108.68 116.06 1925 1
## y_rep[32] 152.51 0.13 5.93 145.19 152.51 160.38 1992 1
## y_rep[33] 160.21 0.13 5.70 152.75 160.16 167.42 1938 1
## y_rep[34] 148.96 0.13 5.68 141.76 148.96 156.12 2016 1
## y_rep[35] 150.61 0.12 5.64 143.44 150.75 157.70 2152 1
## y_rep[36] 157.98 0.13 5.72 150.52 158.05 165.16 2067 1
## y_rep[37] 150.70 0.13 5.86 143.11 150.76 157.99 2028 1
## y_rep[38] 146.62 0.13 5.87 139.28 146.50 154.42 1922 1
## y_rep[39] 158.38 0.14 5.82 150.96 158.34 165.81 1723 1
## y_rep[40] 158.52 0.13 5.78 151.21 158.57 165.86 1888 1
## y_rep[41] 159.41 0.13 5.88 151.95 159.49 166.86 2045 1
## y_rep[42] 159.26 0.13 5.71 151.99 159.34 166.46 1897 1
## y_rep[43] 159.89 0.14 5.72 152.82 159.79 167.33 1691 1
## y_rep[44] 151.40 0.13 6.03 143.64 151.45 159.05 2241 1
## y_rep[45] 159.66 0.13 5.75 152.40 159.61 167.03 1877 1
## y_rep[46] 135.00 0.13 5.80 127.56 135.02 142.29 1965 1
## y_rep[47] 115.55 0.14 5.93 107.96 115.62 123.02 1843 1
## y_rep[48] 122.97 0.13 5.81 115.39 122.96 130.29 1929 1
## y_rep[49] 94.57 0.13 5.79 87.20 94.44 101.93 1978 1
## y_rep[50] 153.91 0.13 5.82 146.32 153.72 161.48 2018 1
## y_rep[51] 150.62 0.13 5.82 143.22 150.85 157.85 1980 1
## y_rep[52] 154.76 0.14 5.92 147.23 154.72 162.43 1898 1
## y_rep[53] 156.83 0.14 5.74 149.86 156.62 164.18 1684 1
## y_rep[54] 119.94 0.13 5.83 112.53 119.95 127.44 1900 1
## y_rep[55] 101.20 0.13 5.79 93.83 101.28 108.77 1906 1
## y_rep[56] 93.16 0.13 5.74 85.82 93.22 100.53 1923 1
## y_rep[57] 159.60 0.13 5.79 152.21 159.55 166.96 2019 1
## y_rep[58] 158.17 0.14 5.87 150.57 158.22 165.45 1836 1
## y_rep[59] 156.12 0.12 5.64 148.86 156.22 163.25 2073 1
## y_rep[60] 160.04 0.13 5.95 152.38 160.14 167.61 2140 1
## y_rep[61] 160.20 0.13 5.92 152.78 160.01 167.94 2086 1
## y_rep[62] 157.49 0.14 5.70 150.06 157.53 164.73 1603 1
## y_rep[63] 158.83 0.14 5.84 151.61 158.60 166.30 1847 1
## y_rep[64] 160.52 0.13 5.74 153.27 160.48 168.20 2065 1
## y_rep[65] 158.49 0.13 5.91 150.78 158.47 166.09 2141 1
## y_rep[66] 157.30 0.12 5.80 149.80 157.25 164.74 2271 1
## y_rep[67] 154.86 0.13 5.80 147.64 154.74 162.41 2048 1
## y_rep[68] 147.86 0.13 5.80 140.43 147.86 155.31 2041 1
## y_rep[69] 160.11 0.13 5.77 152.71 160.18 167.07 2025 1
## y_rep[70] 148.73 0.13 5.80 141.15 148.88 156.25 2059 1
## y_rep[71] 125.79 0.13 5.65 118.51 125.98 132.85 1885 1
## y_rep[72] 128.47 0.13 5.83 120.97 128.39 135.94 1898 1
## y_rep[73] 158.86 0.13 5.89 151.22 158.91 166.26 2005 1
## y_rep[74] 149.10 0.13 5.91 141.72 149.16 156.61 2066 1
## y_rep[75] 136.55 0.13 5.83 129.19 136.38 143.93 1913 1
## y_rep[76] 158.37 0.14 5.93 151.10 158.24 166.03 1787 1
## y_rep[77] 158.35 0.12 5.66 151.41 158.39 165.58 2087 1
## y_rep[78] 93.75 0.13 5.75 86.49 93.70 101.11 2087 1
## y_rep[79] 159.84 0.13 5.68 152.53 159.79 167.37 1901 1
## y_rep[80] 149.86 0.13 5.95 142.32 149.87 157.43 1969 1
## y_rep[81] 154.27 0.13 5.83 146.58 154.34 161.73 1951 1
## y_rep[82] 132.41 0.14 5.78 124.77 132.57 139.44 1760 1
## y_rep[83] 158.38 0.14 5.83 150.71 158.53 165.96 1843 1
## y_rep[84] 155.46 0.13 5.70 147.98 155.45 162.67 1895 1
## y_rep[85] 159.77 0.13 5.83 152.53 159.67 167.35 2000 1
## y_rep[86] 151.39 0.15 5.85 144.14 151.21 158.93 1550 1
## y_rep[87] 107.20 0.13 5.87 99.66 107.29 114.61 1963 1
## y_rep[88] 159.70 0.13 5.83 152.12 159.73 167.21 2069 1
## y_rep[89] 151.59 0.12 5.80 144.17 151.55 159.11 2155 1
## y_rep[90] 147.53 0.14 5.97 139.82 147.38 154.90 1884 1
## y_rep[91] 157.80 0.13 5.67 150.42 157.77 165.23 1793 1
## y_rep[92] 154.82 0.13 5.65 147.70 154.82 161.88 1842 1
## y_rep[93] 158.61 0.13 5.70 151.39 158.55 166.10 1977 1
## y_rep[94] 160.14 0.13 5.83 152.51 160.14 167.58 1907 1
## y_rep[95] 111.07 0.12 5.68 104.04 111.02 118.36 2092 1
## y_rep[96] 158.90 0.14 5.93 151.24 158.88 166.44 1737 1
## y_rep[97] 155.10 0.13 5.92 147.29 155.25 162.79 2105 1
## y_rep[98] 145.73 0.14 5.81 138.45 145.65 153.38 1813 1
## y_rep[99] 108.67 0.13 5.89 101.09 108.71 116.13 1963 1
## y_rep[100] 160.19 0.14 5.83 152.93 160.22 167.79 1735 1
## y_rep[101] 132.22 0.13 5.87 124.54 132.07 139.80 2018 1
## y_rep[102] 159.70 0.13 5.70 152.34 159.84 167.03 1887 1
## y_rep[103] 158.18 0.13 5.83 150.71 158.07 165.57 1936 1
## y_rep[104] 153.21 0.13 5.74 146.04 153.10 160.52 1985 1
## y_rep[105] 141.92 0.13 5.79 134.68 141.82 149.32 1892 1
## y_rep[106] 159.94 0.13 5.71 152.68 159.94 167.43 2026 1
## y_rep[107] 155.26 0.13 5.73 148.11 155.31 162.61 2033 1
## y_rep[108] 152.24 0.13 5.91 144.53 152.21 159.84 2050 1
## y_rep[109] 141.75 0.13 5.82 134.30 141.66 149.33 1896 1
## y_rep[110] 106.48 0.13 5.82 98.85 106.39 113.97 2026 1
## y_rep[111] 104.81 0.13 5.90 97.23 104.77 112.41 1926 1
## y_rep[112] 157.42 0.13 5.87 149.67 157.44 164.88 2008 1
## y_rep[113] 153.55 0.13 5.68 146.52 153.44 161.04 1901 1
## y_rep[114] 109.89 0.13 5.62 102.62 109.99 117.14 1925 1
## y_rep[115] 100.25 0.14 5.79 92.59 100.38 107.50 1658 1
## y_rep[116] 88.76 0.13 5.76 81.12 88.57 95.95 1867 1
## y_rep[117] 158.50 0.12 5.73 151.22 158.53 165.96 2101 1
## y_rep[118] 149.17 0.13 5.80 141.77 149.21 156.72 1999 1
## y_rep[119] 156.90 0.15 5.78 149.35 156.93 164.13 1516 1
## y_rep[120] 154.59 0.13 5.77 147.34 154.44 162.06 1901 1
## y_rep[121] 160.44 0.13 5.80 153.07 160.41 167.68 2050 1
## y_rep[122] 160.52 0.13 5.75 153.05 160.49 167.79 2094 1
## y_rep[123] 160.30 0.13 5.81 152.70 160.32 167.49 1885 1
## y_rep[124] 83.23 0.13 5.92 75.72 83.22 90.92 2067 1
## y_rep[125] 154.77 0.13 5.95 147.19 154.87 162.42 2006 1
## y_rep[126] 159.41 0.13 5.86 151.80 159.47 167.07 2101 1
## y_rep[127] 94.17 0.14 5.89 86.70 94.23 101.76 1781 1
## y_rep[128] 154.28 0.13 5.78 146.98 154.07 161.76 1891 1
## y_rep[129] 160.31 0.13 5.82 153.01 160.28 167.89 2013 1
## y_rep[130] 154.34 0.13 5.74 147.15 154.27 161.91 1921 1
## y_rep[131] 112.80 0.13 5.80 105.39 112.85 120.33 1856 1
## y_rep[132] 100.34 0.12 5.63 92.93 100.38 107.78 2147 1
## y_rep[133] 160.38 0.13 5.86 152.86 160.32 168.21 2009 1
## y_rep[134] 159.67 0.14 5.96 152.08 159.81 167.31 1940 1
## y_rep[135] 154.97 0.14 5.71 147.70 155.11 162.18 1711 1
## y_rep[136] 159.29 0.13 5.80 151.85 159.27 166.77 1993 1
## y_rep[137] 150.62 0.14 5.81 143.28 150.57 158.15 1642 1
## y_rep[138] 159.51 0.13 5.75 152.02 159.66 166.76 1905 1
## y_rep[139] 135.91 0.12 5.60 128.83 135.88 143.13 2027 1
## y_rep[140] 159.20 0.13 5.78 151.44 159.37 166.37 1978 1
## y_rep[141] 89.69 0.14 5.96 81.86 89.60 97.44 1887 1
## y_rep[142] 158.51 0.14 5.91 151.00 158.45 166.23 1707 1
## y_rep[143] 151.50 0.13 5.76 144.22 151.46 158.97 1897 1
## y_rep[144] 150.12 0.13 5.69 142.79 150.20 157.37 1921 1
## y_rep[145] 119.78 0.14 5.88 112.13 119.77 127.34 1852 1
## y_rep[146] 148.43 0.13 5.90 140.83 148.34 156.06 1939 1
## y_rep[147] 154.44 0.13 5.78 146.91 154.52 161.63 2020 1
## y_rep[148] 113.89 0.13 5.72 106.56 113.74 121.23 1851 1
## y_rep[149] 105.56 0.14 6.01 97.87 105.28 113.32 1957 1
## y_rep[150] 156.73 0.13 5.93 148.80 156.79 164.38 2081 1
## y_rep[151] 158.60 0.13 5.68 151.36 158.78 165.74 1960 1
## y_rep[152] 117.36 0.13 5.77 109.95 117.36 124.86 1913 1
## y_rep[153] 111.41 0.14 5.92 103.90 111.30 119.14 1885 1
## y_rep[154] 160.41 0.13 5.65 153.18 160.50 167.77 1783 1
## y_rep[155] 142.72 0.14 5.73 135.49 142.83 149.89 1791 1
## y_rep[156] 153.32 0.13 5.73 145.86 153.22 160.98 1979 1
## y_rep[157] 94.97 0.13 5.88 87.40 94.95 102.27 1976 1
## y_rep[158] 159.83 0.12 5.80 152.47 159.89 167.23 2181 1
## y_rep[159] 159.29 0.13 5.90 151.99 159.27 166.72 2035 1
## y_rep[160] 160.48 0.13 5.88 152.90 160.46 167.97 2020 1
## y_rep[161] 160.34 0.13 5.73 152.84 160.46 167.48 2013 1
## y_rep[162] 160.06 0.13 5.85 152.48 160.25 167.56 2042 1
## y_rep[163] 154.70 0.13 5.94 147.17 154.81 162.22 1972 1
## y_rep[164] 120.72 0.13 5.74 113.24 120.61 128.17 1868 1
## y_rep[165] 153.64 0.14 5.81 146.37 153.64 161.15 1787 1
## y_rep[166] 159.33 0.13 5.63 152.15 159.36 166.53 1897 1
## y_rep[167] 156.32 0.14 5.87 148.90 156.31 163.79 1765 1
## y_rep[168] 157.77 0.12 5.78 150.48 157.68 165.35 2167 1
## y_rep[169] 154.42 0.13 5.90 146.87 154.45 161.81 2067 1
## y_rep[170] 159.99 0.13 5.69 152.78 159.78 167.14 1956 1
## y_rep[171] 93.32 0.13 5.69 86.11 93.29 100.55 1919 1
## y_rep[172] 94.23 0.13 5.66 86.78 94.16 101.39 1961 1
## y_rep[173] 156.21 0.14 5.91 148.59 156.04 164.03 1869 1
## y_rep[174] 141.26 0.13 5.76 133.99 141.29 148.62 2098 1
## y_rep[175] 159.85 0.13 5.97 152.06 160.03 167.46 2014 1
## y_rep[176] 160.23 0.13 5.72 152.74 160.26 167.58 1990 1
## y_rep[177] 147.99 0.13 5.66 140.74 147.92 155.40 2018 1
## y_rep[178] 159.06 0.13 5.57 152.15 158.99 166.21 1965 1
## y_rep[179] 159.85 0.13 5.74 152.56 159.78 167.20 1937 1
## y_rep[180] 154.49 0.13 5.80 146.93 154.56 161.76 2025 1
## y_rep[181] 159.59 0.15 5.89 152.07 159.48 167.07 1546 1
## y_rep[182] 157.96 0.14 5.98 150.16 157.94 165.93 1874 1
## y_rep[183] 158.32 0.13 5.79 151.02 158.32 165.77 1978 1
## y_rep[184] 158.99 0.13 5.79 151.62 159.19 166.13 1918 1
## y_rep[185] 140.16 0.13 5.86 132.60 140.19 147.80 2140 1
## y_rep[186] 141.22 0.13 5.88 133.67 141.37 148.59 1944 1
## y_rep[187] 123.91 0.13 5.79 116.48 123.92 131.12 1876 1
## y_rep[188] 125.47 0.13 5.90 117.79 125.40 133.14 1989 1
## y_rep[189] 118.66 0.13 5.65 111.50 118.80 125.78 1980 1
## y_rep[190] 146.24 0.13 5.84 138.94 146.21 153.75 2095 1
## y_rep[191] 157.37 0.13 5.74 150.12 157.35 164.57 1920 1
## y_rep[192] 156.07 0.13 5.87 148.73 156.07 163.79 1950 1
## y_rep[193] 157.40 0.13 5.81 150.02 157.49 164.74 2007 1
## y_rep[194] 151.13 0.13 5.84 143.55 151.29 158.67 2102 1
## y_rep[195] 153.65 0.12 5.62 146.73 153.50 160.92 2090 1
## y_rep[196] 93.88 0.13 5.94 86.35 93.79 101.49 1970 1
## y_rep[197] 157.47 0.13 5.91 150.03 157.41 165.38 1962 1
## y_rep[198] 160.41 0.14 5.84 152.91 160.44 167.83 1845 1
## y_rep[199] 160.32 0.13 5.67 153.02 160.34 167.69 1895 1
## y_rep[200] 109.74 0.13 5.73 102.30 109.86 116.96 1912 1
## y_rep[201] 96.42 0.14 5.91 89.13 96.39 103.98 1897 1
## y_rep[202] 151.46 0.13 5.71 144.16 151.34 158.89 2024 1
## y_rep[203] 92.47 0.13 5.80 84.92 92.56 99.87 2042 1
## y_rep[204] 157.26 0.13 5.74 150.13 157.31 164.48 2023 1
## y_rep[205] 152.67 0.14 5.85 145.26 152.73 160.05 1824 1
## y_rep[206] 160.14 0.14 5.96 152.58 160.07 167.96 1889 1
## y_rep[207] 150.89 0.12 5.70 143.58 150.85 158.44 2086 1
## y_rep[208] 151.43 0.13 5.79 143.90 151.41 158.87 1865 1
## y_rep[209] 156.46 0.13 5.76 149.21 156.41 163.97 1942 1
## y_rep[210] 151.87 0.14 6.01 144.30 151.72 160.02 1729 1
## y_rep[211] 139.15 0.13 5.90 131.55 139.15 146.59 1993 1
## y_rep[212] 157.95 0.13 5.89 150.47 157.91 165.43 2056 1
## y_rep[213] 120.74 0.13 5.95 113.13 120.76 128.34 1975 1
## y_rep[214] 153.08 0.13 5.78 145.78 153.13 160.58 2024 1
## y_rep[215] 159.52 0.13 5.85 151.77 159.46 166.87 2091 1
## y_rep[216] 153.56 0.13 5.90 146.00 153.51 161.24 2010 1
## y_rep[217] 107.76 0.13 5.72 100.31 107.79 115.05 2029 1
## y_rep[218] 160.31 0.13 5.94 152.64 160.23 168.26 2104 1
## y_rep[219] 157.07 0.13 5.74 149.62 156.96 164.44 1853 1
## y_rep[220] 156.83 0.13 5.71 149.40 156.81 164.12 1866 1
## y_rep[221] 98.48 0.13 5.72 90.97 98.37 106.00 2013 1
## y_rep[222] 112.16 0.13 5.81 104.78 112.06 119.69 1917 1
## y_rep[223] 146.95 0.15 5.78 139.57 147.04 154.28 1460 1
## y_rep[224] 156.92 0.13 5.78 149.63 156.82 164.34 2011 1
## y_rep[225] 158.84 0.13 5.75 151.37 158.90 166.21 1929 1
## y_rep[226] 157.45 0.13 5.77 150.22 157.49 164.67 1837 1
## y_rep[227] 116.74 0.13 5.79 109.23 116.81 124.15 2094 1
## y_rep[228] 159.04 0.13 5.76 151.61 158.94 166.46 1843 1
## y_rep[229] 153.50 0.14 5.78 146.29 153.45 160.89 1778 1
## y_rep[230] 150.35 0.14 5.85 142.98 150.38 157.83 1855 1
## y_rep[231] 154.42 0.14 5.72 147.06 154.55 161.80 1682 1
## y_rep[232] 108.22 0.13 5.82 100.85 108.27 115.56 1950 1
## y_rep[233] 150.02 0.13 5.72 142.65 150.04 157.42 2051 1
## y_rep[234] 159.06 0.13 5.59 151.96 159.03 166.04 1954 1
## y_rep[235] 151.06 0.14 5.71 143.91 151.02 158.35 1718 1
## y_rep[236] 151.93 0.13 5.65 144.76 151.99 159.30 1800 1
## y_rep[237] 159.71 0.13 5.82 152.27 159.71 167.14 1945 1
## y_rep[238] 160.53 0.13 5.94 152.98 160.66 168.04 1945 1
## y_rep[239] 157.26 0.13 5.75 149.82 157.33 164.56 1922 1
## y_rep[240] 153.16 0.13 5.81 145.85 153.20 160.62 1998 1
## y_rep[241] 131.56 0.13 5.74 124.15 131.69 138.67 2045 1
## y_rep[242] 151.66 0.12 5.63 144.69 151.68 158.65 2059 1
## y_rep[243] 115.87 0.12 5.72 108.27 115.84 123.06 2230 1
## y_rep[244] 155.32 0.14 5.83 147.64 155.57 162.49 1774 1
## y_rep[245] 140.68 0.14 5.68 133.38 140.75 147.89 1737 1
## y_rep[246] 116.99 0.13 5.88 109.52 116.96 124.59 1941 1
## y_rep[247] 157.29 0.13 5.76 149.86 157.31 164.77 2049 1
## y_rep[248] 149.80 0.13 5.68 142.47 149.74 157.03 1999 1
## y_rep[249] 103.05 0.14 5.96 95.40 103.06 110.84 1763 1
## y_rep[250] 147.33 0.13 5.62 140.31 147.31 154.80 1899 1
## y_rep[251] 153.11 0.13 5.85 145.52 153.16 160.67 2031 1
## y_rep[252] 158.59 0.13 5.70 151.33 158.71 165.90 1909 1
## y_rep[253] 158.43 0.13 5.72 151.00 158.43 165.80 2031 1
## y_rep[254] 157.86 0.14 5.85 150.42 157.74 165.37 1866 1
## y_rep[255] 153.44 0.13 5.91 145.89 153.33 161.02 2058 1
## y_rep[256] 147.90 0.13 5.84 140.48 148.07 155.17 1994 1
## y_rep[257] 155.42 0.13 5.76 147.83 155.53 162.74 2075 1
## y_rep[258] 158.95 0.13 5.73 151.73 159.04 166.06 2055 1
## y_rep[259] 148.14 0.13 5.82 140.86 148.10 155.63 1967 1
## y_rep[260] 160.31 0.13 5.83 152.98 160.19 167.78 2008 1
## y_rep[261] 150.71 0.13 5.65 143.61 150.55 157.81 1975 1
## y_rep[262] 158.34 0.13 5.94 150.74 158.48 165.99 2066 1
## y_rep[263] 147.52 0.14 5.71 140.03 147.48 154.86 1687 1
## y_rep[264] 97.91 0.13 5.69 90.51 98.06 104.94 2013 1
## y_rep[265] 153.60 0.13 5.85 146.16 153.52 161.15 2009 1
## y_rep[266] 100.80 0.12 5.67 93.52 100.81 107.87 2070 1
## y_rep[267] 156.47 0.13 5.79 149.00 156.40 164.02 2051 1
## y_rep[268] 159.70 0.13 5.83 152.19 159.70 167.32 1880 1
## y_rep[269] 160.24 0.13 5.80 152.95 160.11 167.85 2013 1
## y_rep[270] 149.87 0.13 5.69 142.62 149.85 157.16 1983 1
## y_rep[271] 146.67 0.13 5.76 139.20 146.57 154.16 1928 1
## y_rep[272] 159.63 0.15 5.82 152.20 159.85 166.80 1477 1
## y_rep[273] 118.34 0.14 5.92 110.77 118.31 126.06 1825 1
## y_rep[274] 156.39 0.13 5.63 149.22 156.42 163.61 1909 1
## y_rep[275] 156.49 0.14 5.77 149.29 156.45 163.88 1787 1
## y_rep[276] 156.58 0.13 5.76 149.41 156.48 163.88 1917 1
## y_rep[277] 156.61 0.13 5.85 149.28 156.65 164.04 2025 1
## y_rep[278] 152.57 0.13 5.79 145.08 152.46 160.05 1893 1
## y_rep[279] 156.03 0.13 5.77 148.60 156.14 163.37 2083 1
## y_rep[280] 125.59 0.13 5.72 118.31 125.69 132.82 2037 1
## y_rep[281] 144.81 0.14 5.89 137.39 144.73 152.59 1780 1
## y_rep[282] 142.05 0.13 5.75 134.62 142.17 149.32 2079 1
## y_rep[283] 147.18 0.13 5.80 139.75 147.23 154.62 1975 1
## y_rep[284] 159.57 0.13 5.72 152.18 159.61 167.07 2003 1
## y_rep[285] 160.18 0.13 5.85 152.73 160.13 167.54 1941 1
## y_rep[286] 148.79 0.13 5.79 141.59 148.71 156.23 1975 1
## y_rep[287] 152.99 0.13 5.70 145.80 152.83 160.42 2055 1
## y_rep[288] 159.61 0.13 5.77 152.17 159.60 166.93 1873 1
## y_rep[289] 156.14 0.13 5.73 148.79 156.14 163.30 1934 1
## y_rep[290] 144.00 0.13 5.85 136.44 144.02 151.31 2066 1
## y_rep[291] 118.24 0.13 5.93 110.74 118.05 126.03 2016 1
## y_rep[292] 105.20 0.12 5.80 97.77 105.00 112.76 2226 1
## y_rep[293] 159.45 0.13 5.87 151.78 159.39 167.26 1930 1
## y_rep[294] 143.44 0.13 5.89 135.92 143.52 150.79 2041 1
## y_rep[295] 156.05 0.12 5.70 148.71 155.84 163.52 2092 1
## y_rep[296] 158.62 0.14 5.79 151.35 158.56 166.07 1779 1
## y_rep[297] 155.19 0.13 5.69 148.08 155.08 162.32 2010 1
## y_rep[298] 145.43 0.13 5.94 137.80 145.29 153.29 2076 1
## y_rep[299] 124.81 0.13 5.79 117.62 124.58 132.30 2040 1
## y_rep[300] 144.12 0.13 5.80 136.61 144.09 151.41 2005 1
## y_rep[301] 90.80 0.14 5.99 83.31 90.71 98.39 1875 1
## y_rep[302] 153.67 0.12 5.66 146.41 153.76 160.81 2083 1
## y_rep[303] 152.22 0.13 5.89 144.64 152.20 159.80 2041 1
## y_rep[304] 147.17 0.13 5.84 139.56 147.27 154.45 2053 1
## y_rep[305] 160.07 0.13 5.79 152.61 160.00 167.37 1844 1
## y_rep[306] 157.24 0.13 5.80 149.91 157.14 164.83 2154 1
## y_rep[307] 127.57 0.13 5.66 120.37 127.48 134.78 1779 1
## y_rep[308] 101.38 0.13 5.78 93.68 101.33 108.96 2001 1
## y_rep[309] 159.20 0.13 5.72 152.04 159.14 166.59 2062 1
## y_rep[310] 159.49 0.14 5.93 151.85 159.48 166.88 1764 1
## y_rep[311] 155.56 0.14 5.85 148.06 155.55 163.22 1678 1
## y_rep[312] 108.60 0.13 5.82 101.24 108.63 115.87 1978 1
## y_rep[313] 160.16 0.13 5.76 153.11 160.07 167.57 2011 1
## y_rep[314] 159.88 0.13 5.78 152.58 159.84 167.18 2113 1
## y_rep[315] 144.44 0.14 5.69 137.13 144.56 151.74 1669 1
## y_rep[316] 151.67 0.13 5.74 144.45 151.50 158.93 1932 1
## y_rep[317] 159.33 0.14 5.84 152.01 159.27 166.96 1844 1
## y_rep[318] 152.73 0.14 6.03 145.18 152.61 160.54 1793 1
## y_rep[319] 160.01 0.14 5.77 152.87 160.05 167.50 1700 1
## y_rep[320] 152.33 0.13 5.78 145.09 152.34 159.75 1895 1
## y_rep[321] 155.99 0.13 5.82 148.33 156.21 163.40 2130 1
## y_rep[322] 160.35 0.13 5.74 152.80 160.52 167.76 2088 1
## y_rep[323] 156.68 0.14 5.88 149.24 156.80 164.16 1876 1
## y_rep[324] 88.85 0.13 5.70 81.51 88.99 95.90 2024 1
## y_rep[325] 89.91 0.15 5.62 82.63 89.93 97.14 1399 1
## y_rep[326] 69.14 0.13 5.61 62.10 69.16 76.19 1958 1
## y_rep[327] 90.98 0.13 5.75 83.70 91.00 98.34 1992 1
## y_rep[328] 110.02 0.13 5.68 102.74 110.12 117.39 1988 1
## y_rep[329] 88.64 0.13 5.86 81.14 88.74 96.03 1973 1
## y_rep[330] 153.69 0.12 5.63 146.45 153.73 160.90 2126 1
## y_rep[331] 103.94 0.14 5.84 96.46 104.05 111.24 1731 1
## y_rep[332] 72.55 0.13 5.74 65.19 72.50 79.99 2036 1
## y_rep[333] 90.17 0.13 5.84 82.56 90.28 97.58 1898 1
## y_rep[334] 100.25 0.13 5.67 92.94 100.32 107.34 1874 1
## y_rep[335] 83.38 0.13 5.97 75.89 83.32 91.10 2005 1
## y_rep[336] 154.37 0.13 5.82 146.99 154.30 161.84 1939 1
## y_rep[337] 155.05 0.13 5.86 147.54 154.97 162.33 1974 1
## y_rep[338] 135.18 0.13 5.87 127.43 135.17 143.07 1988 1
## y_rep[339] 93.11 0.13 5.78 85.66 93.24 100.39 1906 1
## y_rep[340] 155.11 0.13 5.86 147.51 155.24 162.55 1990 1
## y_rep[341] 153.17 0.14 5.79 145.83 153.22 160.38 1802 1
## y_rep[342] 155.02 0.13 5.80 147.42 155.11 162.46 1991 1
## y_rep[343] 157.74 0.13 5.84 150.12 157.70 165.61 1985 1
## y_rep[344] 116.10 0.13 5.79 108.51 116.07 123.62 2010 1
## y_rep[345] 102.84 0.13 5.83 95.39 102.70 110.47 1970 1
## y_rep[346] 158.92 0.14 5.92 151.34 159.03 166.35 1814 1
## y_rep[347] 155.02 0.12 5.71 147.68 154.98 162.47 2132 1
## y_rep[348] 106.17 0.13 5.82 98.82 106.06 113.86 2116 1
## y_rep[349] 94.69 0.13 5.77 87.19 94.76 102.35 2106 1
## y_rep[350] 159.02 0.13 5.88 151.37 158.98 166.57 2035 1
## y_rep[351] 157.60 0.13 5.79 150.29 157.44 165.13 1980 1
## y_rep[352] 160.21 0.13 5.75 152.88 160.20 167.60 1953 1
## y_rep[353] 158.39 0.13 5.72 151.19 158.26 165.93 1904 1
## y_rep[354] 93.48 0.13 5.76 86.16 93.39 100.99 1972 1
## y_rep[355] 68.28 0.14 6.00 60.41 68.30 75.92 1873 1
## y_rep[356] 135.15 0.13 5.85 127.64 135.13 142.71 2024 1
## y_rep[357] 155.86 0.13 5.74 148.52 155.78 163.29 1893 1
## y_rep[358] 155.88 0.13 5.83 148.28 155.90 163.28 1963 1
## y_rep[359] 88.79 0.13 5.77 81.53 88.85 96.21 2024 1
## y_rep[360] 89.62 0.13 5.87 82.16 89.57 97.37 1998 1
## y_rep[361] 75.32 0.14 5.91 67.69 75.49 82.72 1860 1
## y_rep[362] 92.82 0.13 5.65 85.60 92.91 100.01 1987 1
## y_rep[363] 74.05 0.14 5.71 66.87 73.96 81.17 1553 1
## y_rep[364] 91.97 0.13 5.82 84.47 91.85 99.43 1943 1
## y_rep[365] 76.03 0.14 6.03 68.12 76.24 83.58 1833 1
## y_rep[366] 160.35 0.13 5.93 153.00 160.20 168.17 2014 1
## y_rep[367] 156.70 0.13 5.76 149.33 156.66 164.20 1976 1
## y_rep[368] 92.28 0.13 5.75 84.72 92.47 99.60 2105 1
## y_rep[369] 92.81 0.13 5.84 85.43 92.82 100.33 2057 1
## y_rep[370] 74.67 0.13 5.84 67.23 74.66 82.08 1989 1
## y_rep[371] 81.05 0.13 5.85 73.51 81.18 88.52 1964 1
## y_rep[372] 158.10 0.14 5.82 150.35 157.98 165.62 1837 1
## y_rep[373] 134.57 0.13 5.73 127.01 134.56 141.93 1934 1
## y_rep[374] 140.36 0.14 5.68 133.15 140.40 147.63 1728 1
## y_rep[375] 160.22 0.14 5.81 152.87 160.12 167.78 1622 1
## y_rep[376] 114.34 0.13 5.85 106.83 114.13 121.97 1884 1
## y_rep[377] 78.55 0.14 5.77 71.13 78.47 85.81 1799 1
## y_rep[378] 78.13 0.13 5.67 70.92 78.15 85.32 1849 1
## y_rep[379] 89.33 0.14 5.82 81.84 89.43 96.84 1667 1
## y_rep[380] 160.24 0.13 5.90 152.56 160.15 168.13 2098 1
## y_rep[381] 76.56 0.13 5.86 69.09 76.49 84.08 2077 1
## y_rep[382] 131.83 0.13 5.73 124.29 131.99 139.39 2028 1
## y_rep[383] 158.39 0.13 5.74 150.90 158.23 165.81 1829 1
## y_rep[384] 86.71 0.14 5.79 79.37 86.67 94.06 1775 1
## y_rep[385] 97.05 0.13 5.70 89.66 97.04 104.37 1942 1
## y_rep[386] 156.90 0.13 5.74 149.54 156.94 164.15 1945 1
## y_rep[387] 157.34 0.13 5.92 149.80 157.14 164.98 1954 1
## y_rep[388] 159.13 0.13 5.68 151.92 158.99 166.45 2012 1
## y_rep[389] 157.90 0.14 5.95 150.56 157.92 165.62 1888 1
## y_rep[390] 114.99 0.13 5.88 107.53 114.79 122.70 2042 1
## y_rep[391] 109.45 0.13 5.78 101.98 109.46 116.82 1924 1
## y_rep[392] 87.01 0.13 5.79 79.35 87.10 94.50 1990 1
## y_rep[393] 156.02 0.14 5.62 148.92 155.96 163.06 1730 1
## y_rep[394] 131.63 0.13 5.82 124.42 131.41 139.13 1954 1
## y_rep[395] 111.90 0.13 5.93 104.14 111.96 119.40 1991 1
## y_rep[396] 96.69 0.13 5.69 89.47 96.69 104.15 1870 1
## y_rep[397] 160.23 0.13 5.78 152.91 160.18 167.61 1903 1
## y_rep[398] 152.57 0.12 5.70 145.20 152.61 159.86 2087 1
## y_rep[399] 130.14 0.14 5.78 122.59 130.16 137.71 1755 1
## y_rep[400] 159.87 0.13 5.75 152.57 159.75 167.38 1855 1
## y_rep[401] 81.16 0.14 5.77 73.76 81.08 88.44 1801 1
## y_rep[402] 75.23 0.13 5.76 68.26 75.23 82.72 1891 1
## y_rep[403] 157.84 0.14 5.74 150.51 157.76 165.10 1764 1
## y_rep[404] 112.72 0.12 5.63 105.48 112.69 120.03 2236 1
## y_rep[405] 149.88 0.13 5.64 142.51 149.91 157.39 1956 1
## y_rep[406] 159.25 0.13 5.65 151.88 159.35 166.32 1825 1
## y_rep[407] 74.26 0.13 5.90 66.57 74.20 81.81 1926 1
## y_rep[408] 133.48 0.12 5.67 126.23 133.48 140.61 2166 1
## y_rep[409] 76.15 0.13 5.90 68.69 76.09 83.86 2021 1
## y_rep[410] 156.44 0.13 5.80 148.86 156.47 163.81 1930 1
## y_rep[411] 159.86 0.15 5.82 152.50 159.78 167.24 1477 1
## y_rep[412] 153.11 0.13 5.68 145.48 153.17 160.21 2010 1
## y_rep[413] 149.19 0.13 5.70 141.92 149.13 156.49 1909 1
## y_rep[414] 160.26 0.13 5.90 152.80 160.26 167.77 2049 1
## y_rep[415] 156.66 0.13 5.75 149.42 156.81 163.89 1892 1
## y_rep[416] 76.84 0.13 5.69 69.55 76.72 84.32 2013 1
## y_rep[417] 155.42 0.14 5.81 148.03 155.41 162.90 1724 1
## y_rep[418] 158.08 0.13 5.90 150.49 158.04 165.63 2018 1
## y_rep[419] 151.61 0.13 5.73 144.27 151.61 159.17 1864 1
## y_rep[420] 145.46 0.13 5.80 137.78 145.52 152.93 1979 1
## y_rep[421] 121.72 0.13 5.89 114.32 121.46 129.44 2151 1
## y_rep[422] 151.13 0.14 5.78 143.94 151.13 158.66 1801 1
## y_rep[423] 149.24 0.13 5.91 141.60 149.23 156.75 2122 1
## y_rep[424] 159.01 0.13 5.89 151.91 158.81 166.61 2020 1
## y_rep[425] 146.59 0.13 5.76 139.30 146.60 153.96 1858 1
## y_rep[426] 81.73 0.14 5.90 74.25 81.80 89.36 1816 1
## y_rep[427] 156.08 0.13 5.76 148.71 156.16 163.61 1989 1
## y_rep[428] 158.92 0.14 5.82 151.25 158.89 166.33 1799 1
## y_rep[429] 136.87 0.13 5.84 129.35 137.01 144.17 1931 1
## y_rep[430] 160.03 0.14 5.80 152.59 159.92 167.40 1831 1
## y_rep[431] 156.17 0.13 5.66 149.14 156.18 163.20 1844 1
## y_rep[432] 133.79 0.13 5.89 126.30 133.72 141.26 2064 1
## y_rep[433] 115.32 0.13 5.96 107.69 115.41 122.99 2163 1
## y_rep[434] 158.56 0.13 5.79 151.08 158.54 166.01 2042 1
## y_rep[435] 151.45 0.13 5.85 144.07 151.36 159.03 1977 1
## y_rep[436] 158.00 0.13 5.66 150.84 157.91 165.45 1849 1
## y_rep[437] 160.05 0.13 5.80 152.80 160.15 167.49 1949 1
## y_rep[438] 158.93 0.13 5.71 151.36 158.94 166.30 1984 1
## y_rep[439] 159.01 0.13 5.87 151.71 158.84 166.55 1898 1
## y_rep[440] 94.94 0.13 5.76 87.69 94.85 102.37 2070 1
## y_rep[441] 71.81 0.12 5.74 64.54 71.86 79.16 2170 1
## y_rep[442] 158.42 0.13 5.73 151.16 158.44 165.75 2067 1
## y_rep[443] 146.57 0.13 5.91 139.04 146.53 154.22 2205 1
## y_rep[444] 148.05 0.12 5.69 140.88 147.96 155.47 2135 1
## y_rep[445] 159.18 0.14 5.72 151.88 159.18 166.52 1753 1
## y_rep[446] 160.12 0.13 5.86 152.62 160.08 167.53 2021 1
## y_rep[447] 158.20 0.13 5.87 150.56 158.19 165.85 1990 1
## y_rep[448] 148.56 0.13 5.69 141.02 148.58 155.93 1835 1
## y_rep[449] 126.87 0.14 5.75 119.39 126.99 134.32 1805 1
## y_rep[450] 103.95 0.13 5.79 96.43 103.98 111.14 2015 1
## y_rep[451] 159.22 0.13 5.77 151.71 159.18 166.56 2069 1
## y_rep[452] 150.10 0.13 5.74 142.72 150.06 157.52 2087 1
## y_rep[453] 78.69 0.13 5.92 70.95 78.54 86.42 2003 1
## y_rep[454] 158.17 0.13 5.76 150.82 158.24 165.41 1855 1
## y_rep[455] 133.97 0.13 5.72 126.57 133.99 141.43 2015 1
## y_rep[456] 77.44 0.13 5.74 70.13 77.48 84.84 1971 1
## y_rep[457] 73.98 0.13 5.84 66.76 74.05 81.48 1997 1
## y_rep[458] 160.54 0.13 5.91 152.74 160.64 167.93 2023 1
## y_rep[459] 141.61 0.13 5.77 134.17 141.57 148.97 2071 1
## y_rep[460] 160.34 0.14 6.02 152.70 160.31 167.88 1925 1
## y_rep[461] 159.15 0.12 5.70 151.72 158.97 166.61 2079 1
## y_rep[462] 155.17 0.14 5.59 147.93 155.32 162.13 1690 1
## y_rep[463] 74.15 0.13 5.89 66.96 74.14 81.82 1991 1
## y_rep[464] 144.75 0.13 5.83 137.13 144.59 152.06 1954 1
## y_rep[465] 159.85 0.13 5.78 152.36 159.89 167.35 1980 1
## y_rep[466] 153.70 0.13 5.80 146.26 153.73 160.92 2041 1
## y_rep[467] 65.02 0.14 5.92 57.51 64.90 72.67 1858 1
## y_rep[468] 70.59 0.14 5.89 63.23 70.59 78.11 1729 1
## y_rep[469] 156.35 0.12 5.80 148.94 156.32 163.78 2225 1
## y_rep[470] 143.53 0.13 5.75 136.12 143.64 150.65 1953 1
## y_rep[471] 106.05 0.13 5.69 98.82 105.97 113.20 1943 1
## y_rep[472] 77.56 0.13 5.94 69.92 77.52 85.24 2248 1
## y_rep[473] 158.44 0.13 5.62 151.44 158.40 165.73 1792 1
## y_rep[474] 157.68 0.13 5.70 150.49 157.82 164.90 1828 1
## y_rep[475] 114.91 0.13 5.79 107.39 115.01 122.09 1877 1
## y_rep[476] 92.94 0.13 5.84 85.33 93.14 100.44 1882 1
## y_rep[477] 158.40 0.13 5.74 151.20 158.32 165.73 1930 1
## y_rep[478] 153.18 0.13 5.69 145.68 153.20 160.57 2064 1
## y_rep[479] 159.72 0.13 5.85 152.13 159.81 167.19 1883 1
## y_rep[480] 156.95 0.13 5.78 149.41 157.17 164.30 2015 1
## y_rep[481] 89.53 0.13 5.72 82.35 89.45 96.70 1904 1
## y_rep[482] 154.44 0.13 5.81 146.93 154.58 161.91 2030 1
## y_rep[483] 154.05 0.12 5.63 146.93 154.02 161.32 2063 1
## y_rep[484] 81.09 0.13 5.61 73.86 81.12 88.21 1745 1
## y_rep[485] 156.94 0.13 5.75 149.42 156.94 164.30 2074 1
## y_rep[486] 160.02 0.13 5.75 153.04 159.79 167.62 2084 1
## y_rep[487] 117.67 0.13 5.70 110.36 117.55 124.89 1927 1
## y_rep[488] 89.18 0.13 5.92 81.45 89.17 96.76 2036 1
## y_rep[489] 159.39 0.13 5.76 151.89 159.54 166.70 2029 1
## y_rep[490] 133.39 0.13 5.79 125.92 133.48 140.78 1917 1
## y_rep[491] 160.06 0.14 5.90 152.51 160.01 167.57 1748 1
## y_rep[492] 155.99 0.13 5.86 148.22 156.12 163.54 1915 1
## y_rep[493] 108.06 0.13 5.79 100.61 108.02 115.60 1842 1
## y_rep[494] 146.26 0.13 5.81 138.75 146.21 153.91 2086 1
## y_rep[495] 144.56 0.14 5.83 137.25 144.35 152.46 1825 1
## y_rep[496] 155.10 0.13 5.73 148.06 154.84 162.58 2059 1
## y_rep[497] 141.85 0.13 5.83 134.53 141.82 149.46 2041 1
## y_rep[498] 158.07 0.13 5.80 150.37 158.09 165.33 2036 1
## y_rep[499] 154.18 0.13 5.78 146.76 154.15 161.61 2039 1
## y_rep[500] 149.99 0.13 5.75 142.57 149.92 157.51 1964 1
## y_rep[501] 155.60 0.13 5.81 148.07 155.68 163.13 2094 1
## y_rep[502] 160.43 0.13 5.85 152.67 160.46 167.89 2160 1
## y_rep[503] 155.46 0.13 5.75 148.21 155.39 162.78 2032 1
## y_rep[504] 118.44 0.13 5.91 110.96 118.48 126.05 1938 1
## y_rep[505] 88.81 0.13 5.79 81.53 88.84 96.38 1954 1
## y_rep[506] 152.15 0.13 5.75 145.01 152.14 159.35 2054 1
## y_rep[507] 155.58 0.12 5.61 148.23 155.49 162.77 2212 1
## y_rep[508] 101.68 0.13 5.81 94.24 101.76 108.82 2037 1
## y_rep[509] 119.50 0.14 5.80 111.94 119.68 126.66 1765 1
## y_rep[510] 160.24 0.13 5.74 152.76 160.41 167.57 1870 1
## y_rep[511] 150.51 0.14 5.72 142.96 150.50 158.02 1794 1
## y_rep[512] 112.59 0.14 5.83 105.33 112.48 119.89 1774 1
## y_rep[513] 87.53 0.13 5.71 80.27 87.53 94.69 1840 1
## y_rep[514] 95.51 0.13 5.74 88.06 95.61 102.72 1984 1
## y_rep[515] 155.28 0.12 5.75 147.92 155.19 162.78 2172 1
## y_rep[516] 147.15 0.12 5.68 139.74 147.24 154.21 2162 1
## y_rep[517] 156.18 0.12 5.68 149.09 156.18 163.32 2134 1
## y_rep[518] 62.99 0.13 5.82 55.64 62.87 70.50 2062 1
## y_rep[519] 149.95 0.13 5.74 142.69 149.83 157.47 2014 1
## y_rep[520] 66.28 0.12 5.61 59.07 66.25 73.38 2124 1
## y_rep[521] 97.97 0.13 5.96 90.37 97.95 105.60 2138 1
## y_rep[522] 122.72 0.13 5.94 115.06 122.80 130.41 2074 1
## y_rep[523] 86.16 0.13 5.85 78.55 86.22 93.52 1974 1
## y_rep[524] 156.05 0.13 5.73 148.80 156.03 163.43 1910 1
## y_rep[525] 156.10 0.13 5.78 148.95 155.85 163.80 1959 1
## y_rep[526] 126.71 0.13 5.76 119.57 126.60 134.41 2023 1
## y_rep[527] 121.10 0.13 5.85 113.78 121.20 128.52 1905 1
## y_rep[528] 98.14 0.12 5.66 90.69 98.25 105.46 2192 1
## y_rep[529] 158.62 0.14 5.69 151.28 158.54 165.82 1644 1
## y_rep[530] 151.94 0.13 5.64 144.65 151.90 159.13 1962 1
## y_rep[531] 126.23 0.12 5.72 118.89 126.23 133.47 2159 1
## y_rep[532] 85.78 0.15 5.81 78.49 85.82 92.97 1470 1
## y_rep[533] 153.42 0.12 5.70 146.12 153.38 160.78 2130 1
## y_rep[534] 153.09 0.13 5.76 145.72 153.16 160.24 2040 1
## y_rep[535] 158.27 0.14 5.63 150.95 158.47 165.33 1726 1
## y_rep[536] 107.75 0.13 5.74 100.34 107.70 115.04 1927 1
## y_rep[537] 74.20 0.13 5.81 66.85 74.07 81.90 1954 1
## y_rep[538] 144.48 0.13 5.76 137.32 144.36 152.03 1911 1
## y_rep[539] 77.16 0.13 5.91 69.68 77.07 84.70 2088 1
## y_rep[540] 139.17 0.13 5.72 131.85 139.21 146.33 1875 1
## y_rep[541] 160.10 0.13 5.80 152.85 160.12 167.48 1859 1
## y_rep[542] 160.40 0.13 5.74 153.02 160.38 167.62 1987 1
## y_rep[543] 77.09 0.14 5.68 69.83 77.07 84.42 1659 1
## y_rep[544] 160.17 0.14 5.74 152.91 160.16 167.41 1715 1
## lp__ -1225.61 0.05 1.44 -1227.50 -1225.27 -1224.12 824 1
##
## Samples were drawn using NUTS(diag_e) at Fri Nov 22 15:25:53 2019.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).summary(lm(height~weight.z+I(weight.z^2),data=howell1))##
## Call:
## lm(formula = height ~ weight.z + I(weight.z^2), data = howell1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -19.9689 -3.9794 0.2364 3.9262 19.5182
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 146.6604 0.3748 391.30 <2e-16 ***
## weight.z 21.4149 0.2908 73.64 <2e-16 ***
## I(weight.z^2) -8.4123 0.2822 -29.80 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.766 on 541 degrees of freedom
## Multiple R-squared: 0.9565, Adjusted R-squared: 0.9564
## F-statistic: 5952 on 2 and 541 DF, p-value: < 2.2e-16Figure 4.9 of Statistical rethinking
6 One continious variable + one categorical variable
6.1 Howell 2: subset with only individuals over 18 years old
ggplot(howell2, aes(y = height, x = weight, group = male)) + geom_point() + geom_smooth(method = "lm")
Xmat <- model.matrix(~weight.z + male, howell2)
m8.data <- with(howell2, list(y = height, X = Xmat, nX = ncol(Xmat), n = nrow(howell2)))data {
int<lower=1> n;
int<lower=1> nX;
vector [n] y;
matrix [n,nX] X;
}
parameters {
vector[nX] beta;
real sigma;
}
transformed parameters {
vector[n] mu;
mu = X*beta;
}
model {
y~normal(mu,sigma);
beta ~ normal(0,100);
sigma~cauchy(0,5);
}
generated quantities {
vector[n] log_lik;
for (i in 1:n) {
log_lik[i] = normal_lpdf(y[i] | mu[i], sigma);
}
}fit.m8 <- sampling(m8, data = m8.data, iter = 1000, chains = 4, cores = 4)
print(fit.m8, probs = c(0.10, 0.5, 0.9))## Inference for Stan model: ff983e7d557e1f552144a41483b33c4a.
## 4 chains, each with iter=1000; warmup=500; thin=1;
## post-warmup draws per chain=500, total post-warmup draws=2000.
##
## mean se_mean sd 10% 50% 90% n_eff Rhat
## beta[1] 145.08 0.03 0.81 144.04 145.08 146.14 722 1
## beta[2] 4.14 0.01 0.27 3.80 4.14 4.48 909 1
## beta[3] 6.48 0.02 0.53 5.80 6.49 7.14 725 1
## sigma 4.29 0.00 0.16 4.08 4.28 4.51 1747 1
## mu[1] 159.86 0.01 0.34 159.42 159.86 160.30 1552 1
## mu[2] 146.11 0.01 0.39 145.61 146.11 146.60 1794 1
## mu[3] 143.15 0.01 0.53 142.47 143.15 143.81 1543 1
## mu[4] 163.21 0.01 0.39 162.70 163.20 163.71 1806 1
## mu[5] 149.18 0.01 0.32 148.78 149.18 149.58 1360 1
## mu[6] 169.59 0.02 0.69 168.69 169.60 170.48 1251 1
## mu[7] 147.24 0.01 0.36 146.79 147.24 147.68 1744 1
## mu[8] 164.77 0.01 0.45 164.20 164.77 165.34 1622 1
## mu[9] 145.07 0.01 0.43 144.52 145.07 145.61 1735 1
## mu[10] 164.13 0.01 0.42 163.59 164.14 164.68 1699 1
## mu[11] 154.71 0.02 0.46 154.12 154.70 155.32 760 1
## mu[12] 155.63 0.01 0.45 155.06 155.63 156.21 961 1
## mu[13] 145.82 0.01 0.40 145.31 145.82 146.32 1787 1
## mu[14] 153.30 0.01 0.40 152.80 153.29 153.82 795 1
## mu[15] 144.42 0.01 0.46 143.83 144.42 145.00 1666 1
## mu[16] 160.33 0.01 0.34 159.90 160.34 160.76 1639 1
## mu[17] 156.33 0.01 0.42 155.80 156.33 156.88 1016 1
## mu[18] 147.31 0.01 0.35 146.86 147.31 147.75 1736 1
## mu[19] 160.61 0.01 0.34 160.17 160.61 161.04 1687 1
## mu[20] 150.11 0.01 0.32 149.70 150.11 150.52 1142 1
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## log_lik[205] -2.51 0.00 0.05 -2.58 -2.51 -2.44 1253 1
## log_lik[206] -2.47 0.00 0.05 -2.53 -2.47 -2.41 1516 1
## log_lik[207] -2.46 0.00 0.04 -2.52 -2.46 -2.41 1226 1
## log_lik[208] -2.48 0.00 0.06 -2.55 -2.47 -2.41 1855 1
## log_lik[209] -2.45 0.00 0.05 -2.53 -2.45 -2.39 1779 1
## log_lik[210] -2.44 0.00 0.05 -2.51 -2.44 -2.38 1602 1
## log_lik[211] -2.45 0.00 0.04 -2.50 -2.44 -2.39 1811 1
## log_lik[212] -2.42 0.00 0.04 -2.47 -2.41 -2.36 1860 1
## log_lik[213] -3.74 0.01 0.23 -4.05 -3.73 -3.45 918 1
## log_lik[214] -3.05 0.00 0.09 -3.17 -3.05 -2.94 1525 1
## log_lik[215] -3.16 0.00 0.11 -3.30 -3.16 -3.03 1756 1
## log_lik[216] -3.45 0.00 0.14 -3.63 -3.44 -3.27 1173 1
## log_lik[217] -4.19 0.00 0.18 -4.43 -4.19 -3.96 1794 1
## log_lik[218] -3.12 0.00 0.13 -3.29 -3.11 -2.95 1649 1
## log_lik[219] -3.04 0.00 0.10 -3.18 -3.03 -2.91 1145 1
## log_lik[220] -2.43 0.00 0.05 -2.49 -2.43 -2.37 1226 1
## log_lik[221] -2.51 0.00 0.05 -2.57 -2.50 -2.45 1281 1
## log_lik[222] -2.38 0.00 0.04 -2.43 -2.38 -2.33 1648 1
## log_lik[223] -2.40 0.00 0.04 -2.46 -2.40 -2.35 1297 1
## log_lik[224] -2.99 0.00 0.10 -3.13 -2.99 -2.86 1811 1
## log_lik[225] -3.45 0.00 0.13 -3.62 -3.45 -3.28 1808 1
## log_lik[226] -2.52 0.00 0.05 -2.58 -2.51 -2.45 1065 1
## log_lik[227] -2.66 0.00 0.08 -2.76 -2.66 -2.56 845 1
## log_lik[228] -2.49 0.00 0.07 -2.58 -2.48 -2.41 1599 1
## log_lik[229] -2.38 0.00 0.04 -2.43 -2.38 -2.33 1654 1
## log_lik[230] -2.55 0.00 0.06 -2.62 -2.55 -2.48 1674 1
## log_lik[231] -3.34 0.00 0.12 -3.50 -3.33 -3.20 1742 1
## log_lik[232] -2.39 0.00 0.04 -2.44 -2.39 -2.34 1699 1
## log_lik[233] -2.55 0.00 0.05 -2.62 -2.55 -2.49 1676 1
## log_lik[234] -3.87 0.01 0.24 -4.17 -3.86 -3.56 1505 1
## log_lik[235] -2.47 0.00 0.05 -2.53 -2.47 -2.41 1910 1
## log_lik[236] -2.98 0.00 0.08 -3.08 -2.97 -2.87 1596 1
## log_lik[237] -4.19 0.01 0.20 -4.46 -4.18 -3.94 1233 1
## log_lik[238] -2.53 0.00 0.08 -2.64 -2.52 -2.43 890 1
## log_lik[239] -2.53 0.00 0.05 -2.60 -2.53 -2.47 1018 1
## log_lik[240] -2.92 0.00 0.08 -3.02 -2.92 -2.82 1390 1
## log_lik[241] -2.40 0.00 0.04 -2.45 -2.40 -2.35 1559 1
## log_lik[242] -2.98 0.00 0.11 -3.12 -2.98 -2.85 1050 1
## log_lik[243] -2.42 0.00 0.04 -2.48 -2.42 -2.37 1321 1
## log_lik[244] -2.38 0.00 0.04 -2.43 -2.38 -2.33 1638 1
## log_lik[245] -3.04 0.00 0.11 -3.18 -3.03 -2.90 1071 1
## log_lik[246] -2.56 0.00 0.06 -2.64 -2.56 -2.49 977 1
## log_lik[247] -2.43 0.00 0.04 -2.49 -2.43 -2.38 1702 1
## log_lik[248] -2.43 0.00 0.04 -2.48 -2.43 -2.38 1465 1
## log_lik[249] -2.38 0.00 0.04 -2.43 -2.38 -2.33 1744 1
## log_lik[250] -2.41 0.00 0.04 -2.47 -2.41 -2.36 1555 1
## log_lik[251] -2.79 0.00 0.08 -2.90 -2.79 -2.69 1823 1
## log_lik[252] -2.51 0.00 0.05 -2.58 -2.51 -2.45 1499 1
## log_lik[253] -2.46 0.00 0.04 -2.52 -2.46 -2.41 1331 1
## log_lik[254] -2.47 0.00 0.05 -2.53 -2.47 -2.41 1325 1
## log_lik[255] -3.09 0.01 0.16 -3.29 -3.09 -2.89 801 1
## log_lik[256] -2.41 0.00 0.04 -2.46 -2.40 -2.36 1455 1
## log_lik[257] -2.38 0.00 0.04 -2.43 -2.38 -2.33 1716 1
## log_lik[258] -2.40 0.00 0.04 -2.46 -2.40 -2.34 1676 1
## log_lik[259] -2.72 0.00 0.09 -2.84 -2.71 -2.61 1631 1
## log_lik[260] -3.05 0.00 0.12 -3.21 -3.04 -2.89 1605 1
## log_lik[261] -2.44 0.00 0.04 -2.50 -2.44 -2.38 1552 1
## log_lik[262] -2.39 0.00 0.04 -2.44 -2.39 -2.34 1528 1
## log_lik[263] -2.74 0.00 0.07 -2.84 -2.74 -2.65 931 1
## log_lik[264] -2.38 0.00 0.04 -2.43 -2.38 -2.33 1568 1
## log_lik[265] -2.51 0.00 0.05 -2.58 -2.51 -2.45 1432 1
## log_lik[266] -3.16 0.00 0.10 -3.29 -3.16 -3.04 1080 1
## log_lik[267] -2.65 0.00 0.08 -2.76 -2.64 -2.55 1685 1
## log_lik[268] -2.38 0.00 0.04 -2.43 -2.38 -2.33 1700 1
## log_lik[269] -2.51 0.00 0.06 -2.60 -2.51 -2.43 923 1
## log_lik[270] -2.47 0.00 0.05 -2.53 -2.47 -2.41 1506 1
## log_lik[271] -2.38 0.00 0.04 -2.43 -2.38 -2.33 1756 1
## log_lik[272] -2.38 0.00 0.04 -2.43 -2.38 -2.33 1600 1
## log_lik[273] -2.42 0.00 0.04 -2.48 -2.42 -2.37 1858 1
## log_lik[274] -3.62 0.01 0.18 -3.86 -3.62 -3.40 995 1
## log_lik[275] -2.46 0.00 0.05 -2.53 -2.46 -2.41 1620 1
## log_lik[276] -2.38 0.00 0.04 -2.43 -2.38 -2.33 1661 1
## log_lik[277] -2.51 0.00 0.05 -2.58 -2.51 -2.45 1157 1
## log_lik[278] -2.39 0.00 0.04 -2.44 -2.38 -2.34 1591 1
## log_lik[279] -2.97 0.00 0.09 -3.09 -2.97 -2.87 1403 1
## log_lik[280] -3.05 0.00 0.09 -3.17 -3.04 -2.93 1659 1
## log_lik[281] -3.62 0.00 0.17 -3.83 -3.62 -3.41 1896 1
## log_lik[282] -2.47 0.00 0.06 -2.55 -2.47 -2.40 962 1
## log_lik[283] -3.49 0.00 0.14 -3.67 -3.49 -3.33 1733 1
## log_lik[284] -2.45 0.00 0.04 -2.51 -2.45 -2.39 1587 1
## log_lik[285] -2.57 0.00 0.06 -2.66 -2.57 -2.49 1858 1
## log_lik[286] -3.14 0.00 0.11 -3.29 -3.13 -3.00 1136 1
## log_lik[287] -2.42 0.00 0.04 -2.47 -2.41 -2.36 1737 1
## log_lik[288] -2.40 0.00 0.04 -2.45 -2.40 -2.35 1634 1
## log_lik[289] -3.41 0.00 0.12 -3.57 -3.41 -3.26 1035 1
## log_lik[290] -2.38 0.00 0.04 -2.43 -2.38 -2.33 1715 1
## log_lik[291] -2.47 0.00 0.05 -2.53 -2.47 -2.41 1545 1
## log_lik[292] -2.39 0.00 0.04 -2.44 -2.39 -2.34 1722 1
## log_lik[293] -2.53 0.00 0.05 -2.60 -2.53 -2.46 1560 1
## log_lik[294] -2.42 0.00 0.05 -2.48 -2.42 -2.37 1241 1
## log_lik[295] -2.40 0.00 0.04 -2.46 -2.40 -2.35 1711 1
## log_lik[296] -2.47 0.00 0.05 -2.54 -2.47 -2.40 1618 1
## log_lik[297] -2.39 0.00 0.04 -2.44 -2.38 -2.34 1592 1
## log_lik[298] -3.64 0.01 0.17 -3.86 -3.63 -3.42 832 1
## log_lik[299] -5.65 0.01 0.30 -6.04 -5.64 -5.26 1682 1
## log_lik[300] -2.40 0.00 0.04 -2.45 -2.40 -2.35 1610 1
## log_lik[301] -2.40 0.00 0.04 -2.45 -2.40 -2.35 1586 1
## log_lik[302] -3.23 0.00 0.11 -3.38 -3.23 -3.10 1603 1
## log_lik[303] -2.58 0.00 0.06 -2.66 -2.58 -2.51 1682 1
## log_lik[304] -2.54 0.00 0.05 -2.61 -2.53 -2.47 1545 1
## log_lik[305] -2.40 0.00 0.04 -2.46 -2.40 -2.35 1531 1
## log_lik[306] -2.80 0.00 0.09 -2.92 -2.80 -2.69 1640 1
## log_lik[307] -3.16 0.00 0.10 -3.29 -3.15 -3.03 1600 1
## log_lik[308] -2.49 0.00 0.05 -2.56 -2.49 -2.43 1311 1
## log_lik[309] -2.43 0.00 0.05 -2.50 -2.43 -2.37 1559 1
## log_lik[310] -2.59 0.00 0.07 -2.68 -2.58 -2.50 784 1
## log_lik[311] -2.39 0.00 0.04 -2.44 -2.39 -2.34 1570 1
## log_lik[312] -2.39 0.00 0.04 -2.44 -2.39 -2.34 1519 1
## log_lik[313] -2.41 0.00 0.04 -2.47 -2.41 -2.36 1689 1
## log_lik[314] -2.41 0.00 0.04 -2.47 -2.41 -2.36 1252 1
## log_lik[315] -3.33 0.00 0.12 -3.48 -3.33 -3.19 1493 1
## log_lik[316] -2.45 0.00 0.04 -2.50 -2.44 -2.39 1588 1
## log_lik[317] -15.34 0.02 1.02 -16.67 -15.31 -14.04 1814 1
## log_lik[318] -3.30 0.00 0.11 -3.45 -3.30 -3.16 991 1
## log_lik[319] -2.43 0.00 0.05 -2.49 -2.42 -2.37 1368 1
## log_lik[320] -3.33 0.00 0.11 -3.47 -3.33 -3.19 1329 1
## log_lik[321] -2.38 0.00 0.04 -2.43 -2.38 -2.33 1711 1
## log_lik[322] -4.25 0.01 0.25 -4.56 -4.23 -3.93 847 1
## log_lik[323] -2.39 0.00 0.04 -2.45 -2.39 -2.34 1651 1
## log_lik[324] -2.64 0.00 0.06 -2.72 -2.63 -2.56 1872 1
## log_lik[325] -2.84 0.00 0.07 -2.93 -2.83 -2.74 1056 1
## log_lik[326] -4.21 0.00 0.21 -4.47 -4.20 -3.94 1963 1
## log_lik[327] -4.40 0.01 0.19 -4.65 -4.40 -4.15 1320 1
## log_lik[328] -2.97 0.00 0.09 -3.08 -2.96 -2.86 1409 1
## log_lik[329] -3.13 0.00 0.13 -3.29 -3.12 -2.97 989 1
## log_lik[330] -2.42 0.00 0.05 -2.49 -2.42 -2.36 1078 1
## log_lik[331] -2.89 0.00 0.09 -3.02 -2.89 -2.77 1041 1
## log_lik[332] -3.57 0.00 0.15 -3.77 -3.56 -3.37 1718 1
## log_lik[333] -2.38 0.00 0.04 -2.43 -2.38 -2.33 1644 1
## log_lik[334] -3.35 0.01 0.16 -3.56 -3.34 -3.14 939 1
## log_lik[335] -2.91 0.00 0.08 -3.02 -2.91 -2.81 1121 1
## log_lik[336] -2.69 0.00 0.07 -2.79 -2.69 -2.60 1852 1
## log_lik[337] -2.40 0.00 0.04 -2.45 -2.40 -2.35 1594 1
## log_lik[338] -2.45 0.00 0.04 -2.50 -2.45 -2.39 1406 1
## log_lik[339] -2.60 0.00 0.07 -2.69 -2.60 -2.52 1690 1
## log_lik[340] -2.56 0.00 0.05 -2.63 -2.56 -2.49 1121 1
## log_lik[341] -2.38 0.00 0.04 -2.43 -2.38 -2.33 1715 1
## log_lik[342] -2.55 0.00 0.06 -2.63 -2.55 -2.48 1241 1
## log_lik[343] -3.13 0.00 0.10 -3.26 -3.13 -3.01 1064 1
## log_lik[344] -2.39 0.00 0.04 -2.44 -2.39 -2.34 1739 1
## log_lik[345] -2.48 0.00 0.05 -2.54 -2.48 -2.42 1699 1
## log_lik[346] -2.39 0.00 0.04 -2.45 -2.39 -2.34 1476 1
## log_lik[347] -2.71 0.00 0.06 -2.80 -2.71 -2.63 1464 1
## log_lik[348] -4.94 0.01 0.25 -5.27 -4.93 -4.62 1051 1
## log_lik[349] -2.47 0.00 0.05 -2.54 -2.46 -2.40 1847 1
## log_lik[350] -2.38 0.00 0.04 -2.43 -2.38 -2.33 1683 1
## log_lik[351] -2.42 0.00 0.05 -2.49 -2.42 -2.36 910 1
## log_lik[352] -2.84 0.00 0.09 -2.96 -2.84 -2.74 1745 1
## lp__ -689.28 0.05 1.42 -691.14 -688.97 -687.74 750 1
##
## Samples were drawn using NUTS(diag_e) at Fri Nov 22 15:25:55 2019.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).summary(lm(height~weight.z+male,data=howell2))##
## Call:
## lm(formula = height ~ weight.z + male, data = howell2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -21.7859 -2.5506 0.4669 2.6278 14.1486
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 145.0498 0.8194 177.02 <2e-16 ***
## weight.z 4.1399 0.2678 15.46 <2e-16 ***
## male 6.5003 0.5359 12.13 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.272 on 349 degrees of freedom
## Multiple R-squared: 0.6973, Adjusted R-squared: 0.6955
## F-statistic: 401.9 on 2 and 349 DF, p-value: < 2.2e-166.2 Howell 1: data set with all individuals
howell1$male <- ifelse(howell1$male==1,2,1)
m8.1.data <- list(N = nrow(howell1), height = howell1$height, weight = howell1$weight.z, male = as.integer(howell1$male), n = length(unique(howell1$male)))data { // observed variables
int<lower=1> N; // number of observations
vector[N] height; // response variables
vector[N] weight; // predictor (previously centered)
int<lower=0> n;
int<lower=1,upper=n> male[N];
}
parameters { // unobserved variables
real beta[2]; // parameters: intercept and slope
vector[n] alpha;
real sigma;
}
transformed parameters {
vector[N] mu; // create one variable with predictions for each obs
for (i in 1:N) // loop for all cases
mu[i] = alpha[male[i]] + beta[1]*weight[i] + beta[2]*(weight[i] .* weight[i]);
}
model {
height ~ normal(mu,sigma); // likelihood
alpha ~ normal(178, 100); // prior of the intercept
beta[1] ~ normal(0, 100); // prior of the slope
beta[2] ~ normal(0, 100);
sigma ~ uniform(0,50);
}
fit.m8.1 <- sampling(m8.1, data = m8.1.data, iter = 1000, chains = 4, cores = 4)
print(fit.m8.1, probs = c(0.10, 0.5, 0.9))## Inference for Stan model: 7f6f4063a593c9d5515aafcd1d091662.
## 4 chains, each with iter=1000; warmup=500; thin=1;
## post-warmup draws per chain=500, total post-warmup draws=2000.
##
## mean se_mean sd 10% 50% 90% n_eff Rhat
## beta[1] 20.68 0.01 0.29 20.30 20.67 21.05 650 1.00
## beta[2] -9.13 0.01 0.28 -9.49 -9.13 -8.75 724 1.00
## alpha[1] 145.32 0.01 0.38 144.84 145.33 145.81 1517 1.00
## alpha[2] 149.67 0.02 0.50 149.03 149.66 150.30 1016 1.00
## sigma 5.41 0.00 0.17 5.19 5.40 5.62 2199 1.00
## mu[1] 160.54 0.01 0.36 160.07 160.53 161.02 1845 1.00
## mu[2] 146.52 0.01 0.38 146.04 146.52 146.99 1606 1.00
## mu[3] 139.47 0.01 0.39 138.97 139.46 139.98 1267 1.00
## mu[4] 161.35 0.02 0.47 160.75 161.34 161.97 899 1.00
## mu[5] 151.93 0.01 0.36 151.48 151.93 152.38 2018 1.00
## mu[6] 156.53 0.04 1.07 155.13 156.52 157.93 614 1.00
## mu[7] 148.73 0.01 0.37 148.26 148.74 149.19 1824 1.00
## mu[8] 160.94 0.02 0.57 160.20 160.93 161.70 735 1.00
## mu[9] 144.26 0.01 0.38 143.77 144.27 144.76 1451 1.00
## mu[10] 161.17 0.02 0.53 160.49 161.16 161.87 786 1.00
## mu[11] 156.79 0.01 0.47 156.19 156.77 157.40 1030 1.00
## mu[12] 156.22 0.01 0.42 155.68 156.21 156.76 1434 1.00
## mu[13] 145.91 0.01 0.38 145.42 145.91 146.39 1558 1.00
## mu[14] 156.15 0.01 0.41 155.63 156.14 156.68 1367 1.00
## mu[15] 142.72 0.01 0.39 142.23 142.72 143.22 1375 1.00
## mu[16] 160.79 0.01 0.37 160.33 160.78 161.28 1690 1.00
## mu[17] 157.20 0.01 0.41 156.68 157.19 157.72 1573 1.00
## mu[18] 148.86 0.01 0.37 148.40 148.87 149.32 1840 1.00
## mu[19] 116.42 0.02 0.49 115.78 116.42 117.08 983 1.00
## mu[20] 95.12 0.01 0.47 94.54 95.11 95.71 2330 1.00
## mu[21] 83.45 0.01 0.58 82.71 83.44 84.18 2332 1.00
## mu[22] 160.92 0.01 0.37 160.44 160.90 161.40 1593 1.00
## mu[23] 153.18 0.01 0.36 152.74 153.18 153.63 2025 1.00
## mu[24] 126.69 0.02 0.51 126.01 126.68 127.35 879 1.00
## mu[25] 101.54 0.01 0.42 101.00 101.53 102.07 2081 1.00
## mu[26] 149.50 0.02 0.50 148.87 149.49 150.14 1011 1.00
## mu[27] 148.32 0.01 0.37 147.85 148.33 148.78 1778 1.00
## mu[28] 145.12 0.01 0.38 144.63 145.12 145.61 1503 1.00
## mu[29] 135.14 0.02 0.53 134.46 135.13 135.82 850 1.00
## mu[30] 120.11 0.01 0.38 119.63 120.09 120.60 1285 1.00
## mu[31] 111.46 0.01 0.49 110.82 111.45 112.12 1066 1.00
## mu[32] 155.34 0.01 0.44 154.78 155.33 155.89 1339 1.00
## mu[33] 161.03 0.02 0.56 160.32 161.03 161.77 752 1.00
## mu[34] 147.84 0.01 0.37 147.36 147.84 148.30 1726 1.00
## mu[35] 149.03 0.01 0.37 148.56 149.03 149.49 1859 1.00
## mu[36] 155.68 0.01 0.39 155.19 155.66 156.18 1563 1.00
## mu[37] 149.42 0.01 0.36 148.96 149.42 149.88 1899 1.00
## mu[38] 145.28 0.01 0.38 144.79 145.28 145.76 1513 1.00
## mu[39] 156.03 0.01 0.41 155.52 156.02 156.56 1429 1.00
## mu[40] 160.56 0.01 0.36 160.09 160.55 161.04 1834 1.00
## mu[41] 161.03 0.01 0.38 160.55 161.01 161.52 1495 1.00
## mu[42] 161.02 0.01 0.38 160.54 161.00 161.51 1502 1.00
## mu[43] 160.60 0.02 0.63 159.80 160.59 161.43 696 1.00
## mu[44] 149.74 0.01 0.36 149.28 149.74 150.20 1916 1.00
## mu[45] 156.79 0.01 0.47 156.19 156.77 157.40 1030 1.00
## mu[46] 133.81 0.01 0.39 133.31 133.79 134.31 1179 1.00
## mu[47] 118.58 0.02 0.50 117.94 118.58 119.24 957 1.00
## mu[48] 121.79 0.01 0.38 121.31 121.77 122.27 1248 1.00
## mu[49] 92.90 0.01 0.48 92.29 92.90 93.52 2375 1.00
## mu[50] 156.25 0.01 0.42 155.70 156.24 156.79 1437 1.00
## mu[51] 149.10 0.01 0.37 148.63 149.10 149.55 1866 1.00
## mu[52] 157.26 0.01 0.41 156.74 157.25 157.78 1583 1.00
## mu[53] 158.92 0.01 0.38 158.43 158.91 159.42 1904 1.00
## mu[54] 122.77 0.02 0.51 122.11 122.77 123.43 917 1.00
## mu[55] 99.79 0.01 0.43 99.25 99.78 100.33 2163 1.00
## mu[56] 91.22 0.01 0.50 90.59 91.21 91.84 2393 1.00
## mu[57] 159.69 0.03 0.75 158.73 159.67 160.67 651 1.00
## mu[58] 155.73 0.01 0.39 155.24 155.71 156.24 1543 1.00
## mu[59] 154.30 0.01 0.36 153.84 154.29 154.76 1956 1.00
## mu[60] 156.95 0.02 0.51 156.32 156.94 157.61 932 1.00
## mu[61] 156.86 0.02 0.66 156.03 156.85 157.75 740 1.00
## mu[62] 159.66 0.01 0.37 159.18 159.65 160.14 2008 1.00
## mu[63] 156.27 0.01 0.42 155.74 156.26 156.81 1304 1.00
## mu[64] 161.37 0.01 0.44 160.82 161.36 161.95 992 1.00
## mu[65] 156.12 0.01 0.41 155.60 156.11 156.65 1382 1.00
## mu[66] 155.18 0.01 0.38 154.71 155.16 155.66 1741 1.00
## mu[67] 152.93 0.01 0.36 152.48 152.92 153.37 2030 1.00
## mu[68] 150.86 0.01 0.49 150.25 150.85 151.49 1065 1.00
## mu[69] 160.81 0.02 0.60 160.04 160.80 161.60 717 1.00
## mu[70] 147.44 0.01 0.37 146.97 147.45 147.91 1688 1.00
## mu[71] 128.98 0.02 0.52 128.31 128.97 129.65 864 1.00
## mu[72] 127.10 0.01 0.39 126.62 127.09 127.60 1178 1.00
## mu[73] 160.71 0.01 0.37 160.25 160.69 161.19 1747 1.00
## mu[74] 147.62 0.01 0.37 147.15 147.63 148.09 1705 1.00
## mu[75] 135.35 0.01 0.39 134.86 135.34 135.85 1193 1.00
## mu[76] 160.27 0.01 0.36 159.80 160.27 160.75 1948 1.00
## mu[77] 155.98 0.01 0.40 155.48 155.97 156.51 1447 1.00
## mu[78] 96.12 0.01 0.52 95.43 96.13 96.80 1452 1.00
## mu[79] 160.20 0.03 0.69 159.32 160.19 161.10 671 1.00
## mu[80] 148.36 0.01 0.37 147.89 148.36 148.82 1782 1.00
## mu[81] 152.49 0.01 0.36 152.04 152.49 152.94 2029 1.00
## mu[82] 131.34 0.01 0.39 130.84 131.32 131.83 1167 1.00
## mu[83] 155.94 0.01 0.40 155.44 155.93 156.47 1461 1.00
## mu[84] 157.90 0.01 0.39 157.40 157.90 158.42 1698 1.00
## mu[85] 161.20 0.01 0.39 160.71 161.18 161.71 1313 1.00
## mu[86] 150.02 0.01 0.36 149.56 150.02 150.48 1931 1.00
## mu[87] 110.30 0.01 0.49 109.67 110.29 110.96 1085 1.00
## mu[88] 161.27 0.01 0.40 160.75 161.24 161.79 1232 1.00
## mu[89] 150.08 0.01 0.36 149.62 150.08 150.54 1935 1.00
## mu[90] 146.26 0.01 0.38 145.77 146.26 146.73 1584 1.00
## mu[91] 159.85 0.01 0.37 159.37 159.84 160.33 2011 1.00
## mu[92] 152.81 0.01 0.36 152.36 152.80 153.25 2030 1.00
## mu[93] 160.46 0.01 0.36 159.99 160.45 160.94 1880 1.00
## mu[94] 160.88 0.02 0.59 160.13 160.87 161.65 726 1.00
## mu[95] 109.87 0.01 0.39 109.38 109.86 110.36 1660 1.00
## mu[96] 160.79 0.01 0.37 160.33 160.78 161.28 1690 1.00
## mu[97] 153.25 0.01 0.36 152.80 153.25 153.70 2023 1.00
## mu[98] 144.55 0.01 0.38 144.06 144.56 145.04 1468 1.00
## mu[99] 111.54 0.01 0.49 110.90 111.54 112.20 1064 1.00
## mu[100] 156.19 0.03 0.80 155.16 156.18 157.27 679 1.00
## mu[101] 135.38 0.02 0.53 134.70 135.37 136.05 850 1.00
## mu[102] 156.99 0.02 0.52 156.33 156.97 157.67 902 1.00
## mu[103] 160.30 0.01 0.36 159.83 160.29 160.78 1941 1.00
## mu[104] 151.61 0.01 0.36 151.16 151.61 152.07 2007 1.00
## mu[105] 140.90 0.01 0.39 140.41 140.90 141.41 1308 1.00
## mu[106] 160.41 0.03 0.66 159.57 160.39 161.27 682 1.00
## mu[107] 157.73 0.01 0.40 157.22 157.72 158.24 1665 1.00
## mu[108] 150.62 0.01 0.36 150.16 150.62 151.08 1963 1.00
## mu[109] 140.48 0.01 0.39 139.99 140.47 140.99 1294 1.00
## mu[110] 109.30 0.01 0.49 108.68 109.29 109.95 1104 1.00
## mu[111] 107.43 0.01 0.49 106.80 107.43 108.08 1142 1.00
## mu[112] 159.69 0.01 0.37 159.21 159.68 160.17 2010 1.00
## mu[113] 151.77 0.01 0.36 151.32 151.77 152.23 2013 1.00
## mu[114] 108.26 0.01 0.40 107.77 108.25 108.75 1737 1.00
## mu[115] 103.07 0.01 0.50 102.42 103.07 103.71 1247 1.00
## mu[116] 91.24 0.01 0.55 90.53 91.23 91.94 1600 1.00
## mu[117] 160.45 0.01 0.36 159.98 160.44 160.93 1885 1.00
## mu[118] 147.84 0.01 0.37 147.36 147.84 148.30 1726 1.00
## mu[119] 159.15 0.01 0.37 158.67 159.14 159.65 1947 1.00
## mu[120] 152.81 0.01 0.36 152.36 152.80 153.25 2030 1.00
## mu[121] 161.09 0.02 0.54 160.39 161.09 161.82 765 1.00
## mu[122] 161.31 0.02 0.49 160.69 161.30 161.96 855 1.00
## mu[123] 161.37 0.01 0.44 160.82 161.36 161.95 995 1.00
## mu[124] 85.17 0.01 0.59 84.41 85.17 85.93 1750 1.00
## mu[125] 152.93 0.01 0.36 152.48 152.92 153.37 2030 1.00
## mu[126] 156.72 0.01 0.46 156.14 156.70 157.32 1066 1.00
## mu[127] 96.69 0.01 0.52 96.00 96.69 97.36 1434 1.00
## mu[128] 156.68 0.01 0.42 156.15 156.68 157.22 1495 1.00
## mu[129] 160.78 0.02 0.60 160.01 160.77 161.58 714 1.00
## mu[130] 152.71 0.01 0.36 152.26 152.71 153.16 2031 1.00
## mu[131] 111.46 0.01 0.39 110.97 111.44 111.94 1590 1.00
## mu[132] 103.07 0.01 0.50 102.42 103.07 103.71 1247 1.00
## mu[133] 161.34 0.02 0.47 160.75 161.33 161.97 894 1.00
## mu[134] 161.20 0.01 0.39 160.70 161.17 161.70 1319 1.00
## mu[135] 153.02 0.01 0.36 152.57 153.01 153.46 2028 1.00
## mu[136] 160.95 0.01 0.37 160.47 160.93 161.44 1567 1.00
## mu[137] 149.03 0.01 0.37 148.56 149.03 149.49 1859 1.00
## mu[138] 156.77 0.01 0.47 156.18 156.76 157.38 1040 1.00
## mu[139] 139.15 0.02 0.53 138.47 139.14 139.84 861 1.00
## mu[140] 159.01 0.03 0.83 157.95 159.00 160.09 636 1.00
## mu[141] 87.68 0.01 0.53 87.00 87.67 88.34 2390 1.00
## mu[142] 160.58 0.01 0.36 160.11 160.57 161.06 1823 1.00
## mu[143] 149.92 0.01 0.36 149.47 149.93 150.38 1926 1.00
## mu[144] 152.94 0.01 0.47 152.34 152.93 153.53 1168 1.00
## mu[145] 118.40 0.01 0.38 117.92 118.38 118.88 1332 1.00
## mu[146] 147.04 0.01 0.37 146.56 147.05 147.51 1650 1.00
## mu[147] 152.69 0.01 0.36 152.24 152.68 153.14 2031 1.00
## mu[148] 112.55 0.01 0.39 112.06 112.54 113.04 1544 1.00
## mu[149] 108.28 0.01 0.49 107.66 108.28 108.93 1124 1.00
## mu[150] 158.87 0.01 0.38 158.38 158.85 159.36 1893 1.00
## mu[151] 156.21 0.01 0.42 155.68 156.20 156.74 1336 1.00
## mu[152] 116.27 0.01 0.38 115.79 116.25 116.76 1402 1.00
## mu[153] 114.43 0.02 0.49 113.78 114.42 115.09 1012 1.00
## mu[154] 161.01 0.02 0.56 160.30 161.01 161.76 748 1.00
## mu[155] 141.37 0.01 0.39 140.87 141.37 141.87 1323 1.00
## mu[156] 151.56 0.01 0.36 151.11 151.56 152.01 2005 1.00
## mu[157] 92.90 0.01 0.48 92.29 92.90 93.52 2375 1.00
## mu[158] 161.32 0.01 0.41 160.80 161.30 161.86 1145 1.00
## mu[159] 160.93 0.01 0.37 160.46 160.92 161.42 1580 1.00
## mu[160] 156.97 0.02 0.62 156.21 156.96 157.81 773 1.00
## mu[161] 161.23 0.02 0.51 160.59 161.23 161.92 812 1.00
## mu[162] 160.97 0.02 0.57 160.24 160.97 161.72 740 1.00
## mu[163] 152.79 0.01 0.36 152.34 152.78 153.23 2030 1.00
## mu[164] 119.33 0.01 0.38 118.85 119.31 119.81 1305 1.00
## mu[165] 151.61 0.01 0.36 151.16 151.61 152.07 2007 1.00
## mu[166] 161.09 0.01 0.38 160.61 161.07 161.59 1432 1.00
## mu[167] 154.37 0.01 0.36 153.92 154.37 154.84 1947 1.00
## mu[168] 159.69 0.01 0.37 159.21 159.68 160.17 2010 1.00
## mu[169] 152.54 0.01 0.36 152.09 152.54 152.99 2030 1.00
## mu[170] 157.00 0.02 0.53 156.34 156.99 157.70 885 1.00
## mu[171] 91.22 0.01 0.50 90.59 91.21 91.84 2393 1.00
## mu[172] 92.06 0.01 0.49 91.44 92.06 92.68 2386 1.00
## mu[173] 154.22 0.01 0.36 153.77 154.22 154.68 1963 1.00
## mu[174] 140.05 0.01 0.39 139.56 140.04 140.56 1282 1.00
## mu[175] 160.53 0.02 0.64 159.71 160.51 161.37 691 1.00
## mu[176] 157.02 0.02 0.58 156.30 157.01 157.80 810 1.00
## mu[177] 146.52 0.01 0.38 146.04 146.52 146.99 1606 1.00
## mu[178] 160.88 0.01 0.37 160.41 160.86 161.36 1626 1.00
## mu[179] 160.45 0.02 0.65 159.62 160.44 161.31 685 1.00
## mu[180] 152.66 0.01 0.36 152.21 152.66 153.11 2030 1.00
## mu[181] 161.19 0.01 0.39 160.70 161.16 161.69 1330 1.00
## mu[182] 155.65 0.01 0.39 155.16 155.63 156.15 1573 1.00
## mu[183] 157.55 0.04 0.98 156.27 157.54 158.82 620 1.00
## mu[184] 160.92 0.01 0.37 160.44 160.90 161.40 1593 1.00
## mu[185] 143.22 0.02 0.52 142.55 143.21 143.90 894 1.00
## mu[186] 140.05 0.01 0.39 139.56 140.04 140.56 1282 1.00
## mu[187] 122.75 0.01 0.38 122.27 122.74 123.23 1230 1.00
## mu[188] 128.64 0.02 0.52 127.97 128.64 129.32 866 1.00
## mu[189] 121.50 0.02 0.50 120.85 121.50 122.16 930 1.00
## mu[190] 144.88 0.01 0.38 144.39 144.88 145.37 1488 1.00
## mu[191] 159.52 0.01 0.37 159.04 159.51 160.00 1998 1.00
## mu[192] 154.06 0.01 0.36 153.61 154.06 154.52 1978 1.00
## mu[193] 155.13 0.01 0.38 154.66 155.12 155.61 1757 1.00
## mu[194] 149.61 0.01 0.36 149.15 149.62 150.07 1909 1.00
## mu[195] 151.83 0.01 0.36 151.38 151.82 152.28 2015 1.00
## mu[196] 92.44 0.01 0.49 91.82 92.43 93.06 2381 1.00
## mu[197] 154.95 0.01 0.37 154.48 154.94 155.43 1815 1.00
## mu[198] 161.29 0.02 0.49 160.67 161.29 161.96 846 1.00
## mu[199] 157.03 0.02 0.57 156.32 157.02 157.78 830 1.00
## mu[200] 112.84 0.02 0.49 112.21 112.84 113.50 1039 1.00
## mu[201] 98.82 0.01 0.51 98.14 98.83 99.48 1369 1.00
## mu[202] 149.71 0.01 0.36 149.25 149.71 150.16 1914 1.00
## mu[203] 94.80 0.01 0.53 94.10 94.80 95.48 1493 1.00
## mu[204] 159.55 0.01 0.37 159.07 159.54 160.03 2001 1.00
## mu[205] 151.08 0.01 0.36 150.63 151.08 151.54 1985 1.00
## mu[206] 161.35 0.01 0.42 160.82 161.32 161.89 1097 1.00
## mu[207] 149.23 0.01 0.36 148.76 149.23 149.68 1879 1.00
## mu[208] 154.20 0.01 0.45 153.63 154.20 154.78 1245 1.00
## mu[209] 154.37 0.01 0.36 153.92 154.37 154.84 1947 1.00
## mu[210] 154.51 0.01 0.45 153.95 154.51 155.08 1268 1.00
## mu[211] 138.08 0.01 0.39 137.59 138.07 138.59 1235 1.00
## mu[212] 155.76 0.01 0.40 155.26 155.74 156.27 1533 1.00
## mu[213] 119.69 0.01 0.38 119.21 119.67 120.17 1296 1.00
## mu[214] 155.65 0.01 0.43 155.09 155.64 156.20 1370 1.00
## mu[215] 161.19 0.01 0.39 160.70 161.16 161.69 1330 1.00
## mu[216] 151.93 0.01 0.36 151.48 151.93 152.38 2018 1.00
## mu[217] 110.63 0.01 0.49 110.01 110.63 111.29 1079 1.00
## mu[218] 161.15 0.02 0.53 160.46 161.14 161.85 779 1.00
## mu[219] 154.79 0.01 0.37 154.33 154.78 155.27 1862 1.00
## mu[220] 154.63 0.01 0.37 154.17 154.63 155.11 1907 1.00
## mu[221] 100.92 0.01 0.50 100.26 100.92 101.57 1307 1.00
## mu[222] 114.85 0.02 0.49 114.20 114.84 115.51 1006 1.00
## mu[223] 149.94 0.02 0.49 149.31 149.93 150.58 1024 1.00
## mu[224] 159.27 0.01 0.37 158.79 159.26 159.76 1966 1.00
## mu[225] 160.64 0.01 0.36 160.18 160.63 161.12 1789 1.00
## mu[226] 155.19 0.01 0.38 154.72 155.18 155.67 1736 1.00
## mu[227] 119.64 0.02 0.50 119.00 119.64 120.30 946 1.00
## mu[228] 160.75 0.01 0.37 160.29 160.73 161.23 1722 1.00
## mu[229] 151.85 0.01 0.36 151.40 151.85 152.30 2016 1.00
## mu[230] 148.93 0.01 0.37 148.47 148.94 149.39 1848 1.00
## mu[231] 152.69 0.01 0.36 152.24 152.68 153.14 2031 1.00
## mu[232] 106.54 0.01 0.40 106.04 106.53 107.03 1824 1.00
## mu[233] 148.73 0.01 0.37 148.26 148.74 149.19 1824 1.00
## mu[234] 160.72 0.01 0.37 160.26 160.70 161.20 1741 1.00
## mu[235] 149.52 0.01 0.36 149.06 149.52 149.97 1904 1.00
## mu[236] 155.05 0.01 0.44 154.49 155.04 155.61 1312 1.00
## mu[237] 156.85 0.02 0.49 156.24 156.84 157.48 997 1.00
## mu[238] 161.20 0.02 0.52 160.54 161.20 161.90 798 1.00
## mu[239] 155.15 0.01 0.38 154.68 155.14 155.63 1749 1.00
## mu[240] 151.45 0.01 0.36 150.99 151.45 151.90 2001 1.00
## mu[241] 130.38 0.01 0.39 129.89 130.37 130.88 1166 1.00
## mu[242] 150.08 0.01 0.36 149.62 150.08 150.54 1935 1.00
## mu[243] 114.47 0.01 0.38 113.98 114.45 114.96 1472 1.00
## mu[244] 157.90 0.01 0.39 157.40 157.90 158.42 1698 1.00
## mu[245] 139.47 0.01 0.39 138.97 139.46 139.98 1267 1.00
## mu[246] 119.87 0.02 0.50 119.22 119.86 120.52 944 1.00
## mu[247] 159.40 0.01 0.37 158.92 159.39 159.89 1985 1.00
## mu[248] 148.49 0.01 0.37 148.03 148.50 148.95 1797 1.00
## mu[249] 101.54 0.01 0.42 101.00 101.53 102.07 2081 1.00
## mu[250] 145.99 0.01 0.38 145.50 145.99 146.46 1564 1.00
## mu[251] 151.56 0.01 0.36 151.11 151.56 152.01 2005 1.00
## mu[252] 160.57 0.01 0.36 160.10 160.56 161.05 1829 1.00
## mu[253] 160.49 0.01 0.36 160.02 160.49 160.97 1866 1.00
## mu[254] 155.56 0.01 0.39 155.08 155.55 156.06 1604 1.00
## mu[255] 156.17 0.01 0.42 155.62 156.16 156.71 1428 1.00
## mu[256] 146.67 0.01 0.37 146.19 146.67 147.14 1618 1.00
## mu[257] 157.82 0.01 0.40 157.31 157.81 158.33 1681 1.00
## mu[258] 160.65 0.01 0.36 160.19 160.64 161.13 1783 1.00
## mu[259] 146.82 0.01 0.37 146.34 146.82 147.29 1631 1.00
## mu[260] 160.60 0.02 0.63 159.80 160.59 161.43 696 1.00
## mu[261] 149.26 0.01 0.36 148.80 149.26 149.71 1883 1.00
## mu[262] 160.40 0.01 0.36 159.94 160.40 160.88 1904 1.00
## mu[263] 146.14 0.01 0.38 145.65 146.14 146.61 1575 1.00
## mu[264] 96.22 0.01 0.46 95.64 96.21 96.79 2300 1.00
## mu[265] 151.93 0.01 0.36 151.48 151.93 152.38 2018 1.00
## mu[266] 99.17 0.01 0.44 98.62 99.17 99.72 2190 1.00
## mu[267] 154.65 0.01 0.37 154.19 154.65 155.12 1902 1.00
## mu[268] 161.23 0.01 0.39 160.72 161.21 161.74 1280 1.00
## mu[269] 160.99 0.02 0.57 160.27 160.99 161.74 744 1.00
## mu[270] 148.36 0.01 0.37 147.89 148.36 148.82 1782 1.00
## mu[271] 149.50 0.02 0.50 148.87 149.49 150.14 1011 1.00
## mu[272] 159.76 0.03 0.74 158.81 159.74 160.73 654 1.00
## mu[273] 117.09 0.01 0.38 116.60 117.06 117.57 1374 1.00
## mu[274] 154.43 0.01 0.36 153.97 154.42 154.90 1941 1.00
## mu[275] 158.76 0.01 0.38 158.27 158.75 159.26 1871 1.00
## mu[276] 154.52 0.01 0.37 154.07 154.52 154.99 1929 1.00
## mu[277] 158.90 0.01 0.38 158.41 158.89 159.40 1900 1.00
## mu[278] 151.17 0.01 0.36 150.71 151.17 151.63 1989 1.00
## mu[279] 154.20 0.01 0.36 153.75 154.20 154.66 1965 1.00
## mu[280] 124.30 0.01 0.39 123.82 124.29 124.78 1206 1.00
## mu[281] 143.59 0.01 0.38 143.10 143.59 144.08 1416 1.00
## mu[282] 141.00 0.01 0.39 140.51 140.99 141.50 1311 1.00
## mu[283] 145.79 0.01 0.38 145.30 145.79 146.27 1549 1.00
## mu[284] 161.06 0.01 0.38 160.58 161.04 161.56 1463 1.00
## mu[285] 161.34 0.02 0.47 160.74 161.33 161.97 886 1.00
## mu[286] 151.64 0.01 0.48 151.03 151.63 152.26 1107 1.00
## mu[287] 151.20 0.01 0.36 150.74 151.19 151.66 1990 1.00
## mu[288] 161.25 0.01 0.40 160.74 161.23 161.77 1248 1.00
## mu[289] 158.46 0.01 0.39 157.97 158.46 158.97 1811 1.00
## mu[290] 142.63 0.01 0.39 142.14 142.63 143.13 1372 1.00
## mu[291] 116.79 0.01 0.38 116.31 116.77 117.28 1384 1.00
## mu[292] 103.60 0.01 0.41 103.07 103.59 104.11 1977 1.00
## mu[293] 161.13 0.01 0.38 160.64 161.11 161.63 1390 1.00
## mu[294] 142.32 0.01 0.39 141.83 142.32 142.82 1359 1.00
## mu[295] 158.38 0.01 0.39 157.89 158.38 158.89 1794 1.00
## mu[296] 156.31 0.01 0.42 155.77 156.29 156.85 1283 1.00
## mu[297] 153.21 0.01 0.36 152.76 153.20 153.66 2025 1.00
## mu[298] 148.56 0.02 0.50 147.91 148.55 149.21 985 1.00
## mu[299] 123.57 0.01 0.39 123.09 123.55 124.04 1217 1.00
## mu[300] 142.81 0.01 0.39 142.32 142.81 143.31 1379 1.00
## mu[301] 88.93 0.01 0.52 88.27 88.93 89.58 2397 1.00
## mu[302] 151.93 0.01 0.36 151.48 151.93 152.38 2018 1.00
## mu[303] 154.72 0.01 0.44 154.16 154.72 155.29 1285 1.00
## mu[304] 145.79 0.01 0.38 145.30 145.79 146.27 1549 1.00
## mu[305] 161.29 0.01 0.40 160.78 161.27 161.83 1193 1.00
## mu[306] 155.24 0.01 0.38 154.77 155.23 155.72 1720 1.00
## mu[307] 126.27 0.01 0.39 125.79 126.25 126.76 1184 1.00
## mu[308] 99.53 0.01 0.44 98.98 99.52 100.07 2175 1.00
## mu[309] 156.64 0.01 0.45 156.06 156.62 157.22 1113 1.00
## mu[310] 159.57 0.03 0.77 158.59 159.55 160.57 648 1.00
## mu[311] 153.75 0.01 0.36 153.31 153.75 154.21 2001 1.00
## mu[312] 111.37 0.01 0.49 110.74 111.37 112.03 1067 1.00
## mu[313] 161.37 0.01 0.43 160.83 161.35 161.94 1025 1.00
## mu[314] 161.27 0.01 0.40 160.75 161.24 161.79 1232 1.00
## mu[315] 143.33 0.01 0.39 142.84 143.33 143.83 1403 1.00
## mu[316] 150.02 0.01 0.36 149.56 150.02 150.48 1931 1.00
## mu[317] 159.14 0.03 0.82 158.09 159.12 160.20 638 1.00
## mu[318] 155.34 0.01 0.44 154.78 155.33 155.89 1339 1.00
## mu[319] 161.37 0.01 0.44 160.82 161.36 161.95 999 1.00
## mu[320] 150.65 0.01 0.36 150.19 150.65 151.11 1964 1.00
## mu[321] 158.44 0.01 0.39 157.95 158.44 158.95 1807 1.00
## mu[322] 156.80 0.03 0.68 155.96 156.79 157.71 731 1.00
## mu[323] 154.84 0.01 0.37 154.38 154.84 155.32 1846 1.00
## mu[324] 91.14 0.01 0.55 90.44 91.13 91.85 1603 1.00
## mu[325] 92.21 0.01 0.54 91.51 92.21 92.91 1572 1.00
## mu[326] 66.38 0.02 0.81 65.37 66.38 67.42 1934 1.00
## mu[327] 93.37 0.01 0.53 92.67 93.37 94.07 1537 1.00
## mu[328] 108.42 0.01 0.39 107.93 108.41 108.91 1729 1.00
## mu[329] 86.51 0.01 0.55 85.82 86.50 87.20 2379 1.00
## mu[330] 151.98 0.01 0.36 151.53 151.98 152.43 2019 1.00
## mu[331] 102.32 0.01 0.42 101.78 102.31 102.84 2043 1.00
## mu[332] 69.89 0.02 0.76 68.94 69.89 70.87 2012 1.00
## mu[333] 92.60 0.01 0.54 91.89 92.60 93.30 1560 1.00
## mu[334] 98.37 0.01 0.44 97.81 98.37 98.93 2223 1.00
## mu[335] 85.57 0.01 0.59 84.82 85.58 86.33 1742 1.00
## mu[336] 152.49 0.01 0.36 152.04 152.49 152.94 2029 1.00
## mu[337] 157.36 0.01 0.40 156.85 157.35 157.88 1600 1.00
## mu[338] 138.26 0.02 0.53 137.58 138.25 138.95 856 1.00
## mu[339] 91.31 0.01 0.50 90.68 91.30 91.94 2392 1.00
## mu[340] 157.86 0.01 0.40 157.36 157.85 158.37 1689 1.00
## mu[341] 151.50 0.01 0.36 151.05 151.50 151.96 2003 1.00
## mu[342] 157.64 0.01 0.40 157.13 157.63 158.15 1648 1.00
## mu[343] 155.48 0.01 0.39 155.00 155.47 155.97 1635 1.00
## mu[344] 114.70 0.01 0.38 114.21 114.68 115.19 1465 1.00
## mu[345] 101.19 0.01 0.43 100.65 101.19 101.72 2098 1.00
## mu[346] 160.55 0.01 0.36 160.08 160.54 161.03 1840 1.00
## mu[347] 153.02 0.01 0.36 152.57 153.01 153.46 2028 1.00
## mu[348] 104.79 0.01 0.41 104.27 104.77 105.28 1915 1.00
## mu[349] 96.97 0.01 0.52 96.28 96.97 97.64 1426 1.00
## mu[350] 160.77 0.01 0.37 160.31 160.76 161.26 1703 1.00
## mu[351] 159.64 0.01 0.37 159.16 159.64 160.12 2007 1.00
## mu[352] 161.36 0.02 0.46 160.77 161.35 161.97 914 1.00
## mu[353] 160.44 0.01 0.36 159.97 160.43 160.92 1890 1.00
## mu[354] 91.78 0.01 0.49 91.16 91.77 92.40 2388 1.00
## mu[355] 69.84 0.02 0.76 68.88 69.83 70.80 1839 1.00
## mu[356] 138.38 0.02 0.53 137.70 138.36 139.06 856 1.00
## mu[357] 153.82 0.01 0.36 153.37 153.81 154.28 1997 1.00
## mu[358] 153.73 0.01 0.36 153.28 153.73 154.19 2002 1.00
## mu[359] 91.34 0.01 0.55 90.63 91.33 92.04 1597 1.00
## mu[360] 87.68 0.01 0.53 87.00 87.67 88.34 2390 1.00
## mu[361] 77.04 0.02 0.68 76.18 77.05 77.90 1847 1.00
## mu[362] 91.03 0.01 0.50 90.40 91.02 91.66 2394 1.00
## mu[363] 71.41 0.02 0.74 70.49 71.41 72.35 2048 1.00
## mu[364] 94.23 0.01 0.53 93.53 94.23 94.92 1511 1.00
## mu[365] 73.65 0.02 0.70 72.77 73.65 74.56 2103 1.00
## mu[366] 156.99 0.02 0.61 156.24 156.98 157.81 783 1.00
## mu[367] 154.60 0.01 0.37 154.14 154.59 155.07 1916 1.00
## mu[368] 94.90 0.01 0.53 94.20 94.90 95.58 1490 1.00
## mu[369] 95.37 0.01 0.52 94.68 95.37 96.04 1475 1.00
## mu[370] 72.05 0.02 0.73 71.15 72.05 72.99 2064 1.00
## mu[371] 78.88 0.01 0.64 78.08 78.89 79.70 2232 1.00
## mu[372] 160.29 0.01 0.36 159.82 160.28 160.76 1944 1.00
## mu[373] 133.47 0.01 0.39 132.97 133.46 133.97 1176 1.00
## mu[374] 139.13 0.01 0.39 138.63 139.12 139.64 1258 1.00
## mu[375] 160.64 0.02 0.63 159.84 160.63 161.47 700 1.00
## mu[376] 117.51 0.02 0.49 116.87 117.51 118.17 969 1.00
## mu[377] 80.63 0.01 0.64 79.82 80.64 81.44 1820 1.00
## mu[378] 75.56 0.01 0.68 74.70 75.55 76.43 2150 1.00
## mu[379] 87.38 0.01 0.54 86.71 87.38 88.06 2388 1.00
## mu[380] 160.85 0.02 0.59 160.09 160.85 161.64 723 1.00
## mu[381] 74.29 0.02 0.70 73.41 74.29 75.19 2118 1.00
## mu[382] 130.56 0.01 0.39 130.07 130.55 131.06 1166 1.00
## mu[383] 160.40 0.01 0.36 159.94 160.40 160.88 1904 1.00
## mu[384] 88.88 0.01 0.56 88.16 88.88 89.60 1665 1.00
## mu[385] 95.30 0.01 0.47 94.72 95.30 95.89 2326 1.00
## mu[386] 154.90 0.01 0.37 154.43 154.89 155.37 1831 1.00
## mu[387] 155.11 0.01 0.38 154.64 155.10 155.59 1763 1.00
## mu[388] 156.54 0.01 0.44 155.98 156.53 157.11 1162 1.00
## mu[389] 160.00 0.01 0.36 159.52 159.99 160.49 2001 1.00
## mu[390] 113.48 0.01 0.39 112.99 113.46 113.97 1508 1.00
## mu[391] 112.28 0.02 0.49 111.64 112.27 112.93 1050 1.00
## mu[392] 89.28 0.01 0.56 88.56 89.27 90.00 1655 1.00
## mu[393] 154.06 0.01 0.36 153.61 154.06 154.52 1978 1.00
## mu[394] 134.78 0.02 0.53 134.10 134.77 135.46 850 1.00
## mu[395] 114.85 0.02 0.49 114.20 114.84 115.51 1006 1.00
## mu[396] 94.75 0.01 0.47 94.17 94.74 95.35 2339 1.00
## mu[397] 160.77 0.02 0.60 160.00 160.76 161.57 713 1.00
## mu[398] 150.77 0.01 0.36 150.31 150.77 151.23 1970 1.00
## mu[399] 133.51 0.02 0.53 132.83 133.50 134.18 851 1.00
## mu[400] 156.94 0.02 0.51 156.31 156.93 157.59 941 1.00
## mu[401] 83.23 0.01 0.61 82.44 83.23 84.00 1785 1.00
## mu[402] 77.14 0.02 0.67 76.29 77.15 78.01 1846 1.00
## mu[403] 159.87 0.01 0.37 159.38 159.86 160.35 2010 1.00
## mu[404] 111.53 0.01 0.39 111.05 111.52 112.02 1586 1.00
## mu[405] 152.67 0.01 0.47 152.07 152.65 153.26 1155 1.00
## mu[406] 161.01 0.01 0.38 160.53 161.00 161.51 1508 1.00
## mu[407] 71.84 0.02 0.73 70.93 71.84 72.78 2058 1.00
## mu[408] 136.84 0.02 0.53 136.16 136.84 137.52 852 1.00
## mu[409] 78.10 0.02 0.66 77.26 78.11 78.96 1841 1.00
## mu[410] 154.22 0.01 0.36 153.77 154.22 154.68 1963 1.00
## mu[411] 161.31 0.01 0.41 160.79 161.28 161.84 1174 1.00
## mu[412] 155.79 0.01 0.43 155.24 155.78 156.34 1384 1.00
## mu[413] 147.91 0.01 0.37 147.43 147.91 148.37 1734 1.00
## mu[414] 161.35 0.01 0.42 160.82 161.33 161.91 1079 1.00
## mu[415] 154.69 0.01 0.37 154.23 154.68 155.16 1892 1.00
## mu[416] 74.50 0.02 0.69 73.63 74.50 75.39 2124 1.00
## mu[417] 153.71 0.01 0.36 153.26 153.71 154.17 2004 1.00
## mu[418] 160.07 0.01 0.36 159.59 160.06 160.55 1992 1.00
## mu[419] 150.20 0.01 0.36 149.74 150.21 150.66 1941 1.00
## mu[420] 144.14 0.01 0.38 143.65 144.14 144.63 1444 1.00
## mu[421] 124.74 0.02 0.51 124.07 124.73 125.40 895 1.00
## mu[422] 154.27 0.01 0.45 153.70 154.26 154.84 1250 1.00
## mu[423] 147.77 0.01 0.37 147.29 147.77 148.23 1719 1.00
## mu[424] 160.83 0.01 0.37 160.37 160.81 161.31 1665 1.00
## mu[425] 145.32 0.01 0.38 144.83 145.32 145.80 1516 1.00
## mu[426] 83.84 0.01 0.61 83.06 83.85 84.62 1775 1.00
## mu[427] 158.28 0.01 0.39 157.78 158.28 158.78 1773 1.00
## mu[428] 160.67 0.01 0.37 160.21 160.66 161.15 1771 1.00
## mu[429] 140.18 0.02 0.53 139.50 140.17 140.87 868 1.00
## mu[430] 161.30 0.01 0.41 160.79 161.28 161.83 1183 1.00
## mu[431] 154.14 0.01 0.36 153.69 154.14 154.60 1971 1.00
## mu[432] 137.13 0.02 0.53 136.45 137.12 137.81 853 1.00
## mu[433] 118.43 0.02 0.50 117.79 118.43 119.09 959 1.00
## mu[434] 160.67 0.01 0.37 160.21 160.66 161.15 1771 1.00
## mu[435] 154.14 0.01 0.45 153.57 154.14 154.72 1241 1.00
## mu[436] 160.06 0.01 0.36 159.58 160.05 160.54 1994 1.00
## mu[437] 160.65 0.02 0.62 159.85 160.64 161.47 701 1.00
## mu[438] 160.80 0.01 0.37 160.34 160.79 161.28 1684 1.00
## mu[439] 156.34 0.01 0.43 155.80 156.32 156.88 1267 1.00
## mu[440] 97.34 0.01 0.51 96.65 97.35 98.02 1414 1.00
## mu[441] 69.35 0.02 0.76 68.39 69.35 70.34 2000 1.00
## mu[442] 160.40 0.01 0.36 159.94 160.40 160.88 1904 1.00
## mu[443] 145.24 0.01 0.38 144.75 145.24 145.72 1511 1.00
## mu[444] 146.67 0.01 0.37 146.19 146.67 147.15 1618 1.00
## mu[445] 156.57 0.01 0.45 156.00 156.55 157.14 1149 1.00
## mu[446] 161.33 0.01 0.41 160.81 161.30 161.87 1135 1.00
## mu[447] 159.98 0.01 0.36 159.50 159.97 160.46 2003 1.00
## mu[448] 147.15 0.01 0.37 146.67 147.16 147.62 1660 1.00
## mu[449] 130.29 0.02 0.52 129.62 130.28 130.95 858 1.00
## mu[450] 106.75 0.01 0.49 106.11 106.74 107.39 1157 1.00
## mu[451] 160.82 0.01 0.37 160.36 160.80 161.30 1671 1.00
## mu[452] 148.49 0.01 0.37 148.03 148.50 148.95 1797 1.00
## mu[453] 76.29 0.01 0.67 75.45 76.29 77.15 2168 1.00
## mu[454] 160.32 0.01 0.36 159.85 160.32 160.80 1933 1.00
## mu[455] 132.90 0.01 0.39 132.40 132.89 133.40 1173 1.00
## mu[456] 74.93 0.01 0.69 74.06 74.92 75.81 2134 1.00
## mu[457] 75.75 0.02 0.69 74.87 75.76 76.63 1851 1.00
## mu[458] 160.96 0.02 0.57 160.23 160.96 161.72 739 1.00
## mu[459] 144.87 0.02 0.52 144.21 144.85 145.53 915 1.00
## mu[460] 161.22 0.02 0.51 160.56 161.21 161.91 804 1.00
## mu[461] 160.76 0.01 0.37 160.30 160.75 161.25 1709 1.00
## mu[462] 153.45 0.01 0.36 153.01 153.45 153.91 2017 1.00
## mu[463] 71.62 0.02 0.73 70.71 71.62 72.56 2053 1.00
## mu[464] 143.24 0.01 0.39 142.75 143.25 143.74 1399 1.00
## mu[465] 156.80 0.01 0.48 156.20 156.78 157.41 1024 1.00
## mu[466] 156.30 0.01 0.42 155.75 156.29 156.84 1444 1.00
## mu[467] 62.24 0.02 0.87 61.14 62.23 63.35 1850 1.00
## mu[468] 72.05 0.02 0.73 71.11 72.05 72.98 1849 1.00
## mu[469] 154.37 0.01 0.36 153.92 154.37 154.84 1947 1.00
## mu[470] 142.10 0.01 0.39 141.61 142.10 142.59 1350 1.00
## mu[471] 104.28 0.01 0.41 103.76 104.27 104.78 1942 1.00
## mu[472] 75.24 0.01 0.68 74.38 75.24 76.12 2142 1.00
## mu[473] 160.32 0.01 0.36 159.85 160.32 160.80 1933 1.00
## mu[474] 155.43 0.01 0.38 154.96 155.42 155.93 1651 1.00
## mu[475] 113.63 0.01 0.38 113.14 113.61 114.12 1503 1.00
## mu[476] 95.56 0.01 0.52 94.87 95.56 96.23 1469 1.00
## mu[477] 160.37 0.01 0.36 159.90 160.36 160.85 1917 1.00
## mu[478] 151.53 0.01 0.36 151.08 151.53 151.99 2004 1.00
## mu[479] 161.22 0.01 0.39 160.71 161.19 161.72 1296 1.00
## mu[480] 154.88 0.01 0.37 154.42 154.87 155.36 1836 1.00
## mu[481] 87.38 0.01 0.54 86.71 87.38 88.06 2388 1.00
## mu[482] 157.13 0.01 0.41 156.60 157.12 157.65 1561 1.00
## mu[483] 152.27 0.01 0.36 151.82 152.26 152.71 2026 1.00
## mu[484] 83.02 0.01 0.61 82.23 83.03 83.79 1788 1.00
## mu[485] 159.27 0.01 0.37 158.79 159.26 159.76 1966 1.00
## mu[486] 156.99 0.02 0.52 156.33 156.97 157.67 902 1.00
## mu[487] 120.69 0.02 0.50 120.04 120.69 121.34 937 1.00
## mu[488] 91.63 0.01 0.54 90.92 91.62 92.33 1589 1.00
## mu[489] 160.99 0.01 0.37 160.51 160.98 161.48 1528 1.00
## mu[490] 132.10 0.01 0.39 131.60 132.08 132.59 1169 1.00
## mu[491] 161.32 0.01 0.41 160.80 161.30 161.86 1145 1.00
## mu[492] 154.04 0.01 0.36 153.59 154.04 154.50 1980 1.00
## mu[493] 110.96 0.01 0.49 110.33 110.96 111.62 1074 1.00
## mu[494] 145.20 0.01 0.38 144.71 145.20 145.68 1508 1.00
## mu[495] 143.33 0.01 0.39 142.84 143.33 143.83 1403 1.00
## mu[496] 153.31 0.01 0.36 152.87 153.31 153.77 2022 1.00
## mu[497] 140.62 0.01 0.39 140.13 140.62 141.13 1299 1.00
## mu[498] 160.10 0.01 0.36 159.62 160.09 160.58 1988 1.00
## mu[499] 156.81 0.01 0.41 156.28 156.80 157.34 1513 1.00
## mu[500] 153.02 0.01 0.47 152.42 153.01 153.61 1173 1.00
## mu[501] 157.98 0.01 0.39 157.47 157.97 158.49 1712 1.00
## mu[502] 161.29 0.02 0.49 160.67 161.29 161.96 846 1.00
## mu[503] 153.39 0.01 0.36 152.94 153.38 153.84 2019 1.00
## mu[504] 121.57 0.02 0.50 120.92 121.57 122.23 930 1.00
## mu[505] 86.70 0.01 0.54 86.02 86.70 87.39 2381 1.00
## mu[506] 154.78 0.01 0.44 154.22 154.78 155.35 1290 1.00
## mu[507] 153.67 0.01 0.36 153.22 153.67 154.13 2006 1.00
## mu[508] 99.97 0.01 0.43 99.42 99.96 100.51 2155 1.00
## mu[509] 122.52 0.02 0.50 121.87 122.52 123.18 920 1.00
## mu[510] 161.37 0.01 0.45 160.79 161.36 161.97 939 1.00
## mu[511] 148.96 0.01 0.37 148.50 148.97 149.42 1852 1.00
## mu[512] 111.14 0.01 0.39 110.65 111.13 111.63 1603 1.00
## mu[513] 89.97 0.01 0.56 89.25 89.96 90.68 1636 1.00
## mu[514] 93.65 0.01 0.48 93.05 93.64 94.25 2363 1.00
## mu[515] 153.25 0.01 0.36 152.80 153.25 153.70 2023 1.00
## mu[516] 145.71 0.01 0.38 145.23 145.72 146.20 1544 1.00
## mu[517] 154.30 0.01 0.36 153.84 154.29 154.76 1956 1.00
## mu[518] 59.84 0.02 0.91 58.70 59.83 61.00 1806 1.00
## mu[519] 148.53 0.01 0.37 148.06 148.53 148.98 1801 1.00
## mu[520] 63.48 0.02 0.85 62.40 63.47 64.57 1874 1.00
## mu[521] 100.65 0.01 0.50 99.98 100.66 101.31 1314 1.00
## mu[522] 125.79 0.02 0.51 125.12 125.78 126.45 886 1.00
## mu[523] 84.04 0.01 0.57 83.31 84.04 84.77 2343 1.00
## mu[524] 158.56 0.01 0.38 158.07 158.55 159.06 1831 1.00
## mu[525] 154.16 0.01 0.36 153.71 154.16 154.62 1969 1.00
## mu[526] 129.96 0.02 0.52 129.29 129.96 130.63 860 1.00
## mu[527] 119.90 0.01 0.38 119.42 119.88 120.39 1291 1.00
## mu[528] 96.40 0.01 0.46 95.82 96.39 96.97 2294 1.00
## mu[529] 160.56 0.01 0.36 160.09 160.55 161.04 1834 1.00
## mu[530] 150.05 0.01 0.36 149.59 150.05 150.51 1933 1.00
## mu[531] 125.16 0.01 0.39 124.68 125.14 125.65 1196 1.00
## mu[532] 84.04 0.01 0.57 83.31 84.04 84.77 2343 1.00
## mu[533] 156.06 0.01 0.43 155.51 156.05 156.60 1415 1.00
## mu[534] 151.50 0.01 0.36 151.05 151.50 151.96 2003 1.00
## mu[535] 155.87 0.01 0.40 155.37 155.86 156.39 1489 1.00
## mu[536] 110.46 0.01 0.49 109.84 110.46 111.12 1082 1.00
## mu[537] 71.52 0.02 0.73 70.60 71.51 72.46 2051 1.00
## mu[538] 143.33 0.01 0.39 142.84 143.33 143.83 1403 1.00
## mu[539] 78.84 0.02 0.66 78.02 78.85 79.69 1836 1.00
## mu[540] 142.52 0.02 0.53 141.85 142.51 143.20 887 1.00
## mu[541] 161.37 0.01 0.44 160.82 161.36 161.95 999 1.00
## mu[542] 156.90 0.02 0.65 156.09 156.89 157.77 749 1.00
## mu[543] 78.95 0.02 0.65 78.12 78.96 79.79 1835 1.00
## mu[544] 161.37 0.01 0.45 160.80 161.36 161.96 955 1.00
## lp__ -1189.58 0.06 1.61 -1191.77 -1189.22 -1187.88 694 1.01
##
## Samples were drawn using NUTS(diag_e) at Fri Nov 22 15:25:58 2019.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).